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On co-minimal pairs in abelian groupsJun 13 2019A pair of non-empty subsets $(W,W')$ in an abelian group $G$ is a complement pair if $W+W'=G$. $W'$ is said to be minimal to $W$ if $W+(W'\setminus \{w'\}) \neq G, \forall \,w'\in W'$. In general, given an arbitrary subset in a group, the existence of ... More

Static Spherically Symmetric Einstein-aether models: Integrability and the Modified Tolman-Oppenheimer-Volkoff approachJun 13 2019We study the evolution of the dynamics and the existence of analytic solutions for the field equations in the Einstein-aether theory for a static spherically symmetric spacetime. In particular, we investigate if the gravitational field equations in the ... More

Triple transitivity and non-free actions in dimension oneJun 13 2019We show that if $G$ is either: (1) a group homeomorphisms of the circle such that the action of $G$ on $S^1$ is minimal, proximal, non-topologically free and satisfies some mild assumption; (2) a group of automorphisms of a tree $T$ such that the action ... More

Towards Gaussian states for loop quantum gravityJun 13 2019An important challenge in loop quantum gravity is to find semiclassical states - states that are as close to classical as quantum theory allows. This is difficult because the states in the Hilbert space used in LQG are excitations over a vacuum in which ... More

Between buildings and free factor complexes: A Cohen-Macaulay complex for Out(RAAGs)Jun 13 2019For every finite graph $\Gamma$, we define a simplicial complex associated to the outer automorphism group of the RAAG $A_\Gamma$. These complexes are defined as coset complexes of parabolic subgroups of $Out^0(A_\Gamma)$ and interpolate between Tits ... More

Signed Hultman Numbers and Signed Generalized Commuting Probability in Finite GroupsJun 13 2019Let G be a finite group. Let pi be a permutation from S{n}. We study the distribution of probabilities of equality a{1} a{2} ...a{n-1}a{n}=a{pi{1}}^{epsilon{1}} a{pi_{2}}^{epsilon{2}}...a{pi{n-1}}^{epsilon_{n-1}} a_{pi_{n}}^{epsilon{n}}, when pi varies ... More

Coherency and constructions for monoidsJun 13 2019A monoid $S$ is right coherent if every finitely generated subact of every finitely presented right $S$-act is finitely presented. This is a finiteness condition, and we investigate whether or not it is preserved under some standard algebraic and semigroup ... More

Polish groups of unitariesJun 13 2019We study the question of which Polish groups which can be realized as subgroups of the unitary group of a separable infinite-dimensional Hilbert space. We also show that the unitary group of a separable unital C$^*$-algebra with finite exponential length ... More

Bent walls for random groups in the square and hexagonal modelJun 12 2019We introduce a new random group model, called the hexagonal model, defined as the quotient of a free group by a random set of reduced words of length six. Our first main result is that in this model there exists a sharp density threshold for Kazhdan's ... More

On the group of infinite $p$-adic matrices with integer elementsJun 12 2019Let $G$ be an infinite-dimensional real classical group containing the complete unitary group (or complete orthogonal group) as a subgroup. Then $G$ generates a category of double cosets (train) and any unitary representation of $G$ can be canonically ... More

Polynomially growing harmonic functions on connected groupsJun 12 2019We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. Our main result shows that (for sufficiently "nice" random walk measures) a connected, compactly generated, locally ... More

Homology, lower central series, and hyperplane arrangementsJun 12 2019We explore finitely generated groups by studying the nilpotent towers and the various Lie algebras attached to such groups. Our main goal is to relate an isomorphism extension problem in the Postnikov tower to the existence of certain commuting diagrams. ... More

On the quantum Geroch groupJun 11 2019The Geroch group is an infinite dimensional transitive group of symmetries of cylindrically symmetric gravitational waves which acts by non-canonical transformations on the phase space of these waves. The unique Poisson bracket on the Geroch group which ... More

On the balance problem for two rotating and charged black holesJun 11 2019It is an interesting open problem whether two non-extremal rotating and electrically charged black holes can be in physical equilibrium, which might be possible due to a balance between the gravitational attraction and the spin-spin and electrical repulsions. ... More

Electromagnetic fields on Kerr spacetime, Hertz potentials and Lorentz gaugeJun 11 2019We review two procedures for constructing the vector potential of the electromagnetic field on Kerr spacetime, namely, the classic method of Cohen & Kegeles, yielding $A^\mu$ in a radiation gauge, and the newer method of Frolov et al., yielding $A^\mu$ ... More

Quantization of dynamical symplectic reductionJun 11 2019A long-standing problem in quantum gravity and cosmology is the quantization of systems in which evolution is generated by a constraint that must vanish on solutions. Here, an algebraic formulation of this problem is presented, together with new structures ... More

On pro-$p$ groups with quadratic cohomologyJun 11 2019The main purpose of this article is to study pro-$p$ groups with quadratic $\mathbb{F}_p$-cohomology algebra, i.e. $H^\bullet$-quadratic pro-$p$ groups. Prime examples of such groups are the maximal Galois pro-$p$ groups of fields containing a primitive ... More

Word and Conjugacy Problems in Groups $G_{k+1}^{k}$Jun 11 2019Recently the third named author defined a 2-parametric family of groups $G_n^k$ \cite{gnk}. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between the groups $G_n^k$ and dynamical systems led to the discovery ... More

Schur ring and Codes for $S$-subgroups over $\Z_{2}^{n}$Jun 10 2019In this paper the relationship between $S$-subgroups in $\Z_{2}^{n}$ and binary codes is shown. If the codes used are both $P(T)$-codes and $G$-codes, then the $S$-subgroup is free. The codes constructed are cyclic, decimated or symmetric and the $S$-subgroups ... More

Actions of solvable Baumslag-Solitar groups on hyperbolic metric spacesJun 10 2019We give a complete list of the cobounded actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces up to a natural equivalence relation. The set of equivalence classes carries a natural partial order first introduced by Abbott-Balasubramanya-Osin, ... More

The conjugacy problem for UPG elements of $Out(F_n)$Jun 10 2019$Out(F_n):=Aut(F_n)/Inn(F_n)$ denotes the outer automorphism group of the rank $n$ free group $F_n$. An element $\phi$ of $Out(F_n)$ is polynomially growing if the word lengths of conjugacy classes in $F_n$ grow at most polynomially under iteration by ... More

Weighted Quasi Interpolant Spline Approximation of 3D point clouds via local refinementJun 10 2019We present a new surface approximation, the Weighted Quasi Interpolant Spline Approximation (w-QISA), to approximate very large and noisy point clouds. We adopt local implicit representations based on three key ingredients: 1) a local mesh for the piecewise ... More

Tropical Representations of Plactic MonoidsJun 10 2019We exhibit a faithful representation of the plactic monoid of every finite rank as a monoid of upper triangular matrices over the tropical semiring. This answers a question first posed by Izhakian and subsequently studied by several authors. A consequence ... More

Gravitational perturbations as $T\bar{T}$-deformations in 2D dilaton gravity systemsJun 10 2019We consider gravitational perturbations of 2D dilaton gravity systems and show that these can be recast into $T\bar{T}$-deformations (at least) under certain conditions, where $T$ means the energy-momentum tensor of the matter field coupled to a dilaton ... More

Laplacian Spectral Basis FunctionsJun 10 2019Representing a signal as a linear combination of a set of basis functions is central in a wide range of applications, such as approximation, de-noising, compression, shape correspondence and comparison. In this context, our paper addresses the main aspects ... More

Haagerup property for wreath products constructed with Thompson's groupsJun 10 2019Using recent techniques introduced by Jones we prove that a large family of discrete groups and groupoids have the Haagerup property. In particular, we show that if G is a discrete group with the Haagerup property, then the wreath product $\oplus_{Q_2}G\rtimes ... More

Essential dimension of double covers of symmetric and alternating groupsJun 09 2019I. Schur studied double covers $\widetilde{\Sym}^{\pm}_n$ and $\widetilde{\Alt}_n$ of symmetric groups $\Sym_n$ and alternating groups $\Alt_n$, respectively. Representations of these groups are closely related to projective representations of $\Sym_n$ ... More

Mapping classes are almost determined by their finite quotient actionsJun 09 2019Given any connected compact orientable surface, a pair of mapping classes are said to be procongruently conjugate if they induce a conjugate pair of outer automophisms on every characteristic finite quotient of the fundamental group of the surface. In ... More

Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: ConstructionJun 09 2019Following the recent advances in the study of groups of circle diffeomorphisms, we classify the topological dynamics of locally discrete, finitely generated, virtually free subgroups of the group $\mathsf{Diff}^\omega_+(\mathbb S^1)$ of orientation preserving ... More

Orders of units in integral group rings and blocks of defect $1$Jun 09 2019We show that if the Sylow $p$-subgroup of a finite group $G$ is of order $p$, then the normalized unit group of the integral group ring of $G$ contains a normalized unit of order $pq$ if and only if $G$ contains an element of order $pq$, where $q$ is ... More

Higher spin mapping class groups and strata of Abelian differentials over Teichm{ü}ller spaceJun 08 2019For $g \ge 5$, we give a complete classification of the connected components of strata of abelian differentials over Teichm\"uller space, establishing an analogue of a theorem of Kontsevich and Zorich in the setting of marked translation surfaces. Building ... More

Weil representations via abstract data and Heisenberg groups: a comparisonJun 08 2019Let $B$ be a ring, not necessarily commutative, having an involution $*$ and let ${\mathrm U}_{2m}(B)$ be the unitary group of rank $2m$ associated to a hermitian or skew hermitian form relative to $*$. When $B$ is finite, we construct a Weil representation ... More

An Automaton Group with PSPACE-Complete Word ProblemJun 08 2019We construct an automaton group with a PSPACE-complete word problem, proving a conjecture due to Steinberg. Additionally, the constructed group has a provably more difficult, namely EXPSPACE-complete, compressed word problem. Our construction directly ... More

Rigid representations of triangle groupsJun 07 2019We prove a generalization of a conjecture of C. Marion on generation properties of finite groups of Lie type, by considering geometric properties of an appropriate representation variety and associated tangent spaces.

On the Differentiation Lemma and the Reynolds Transport Theorem for Manifolds with CornersJun 07 2019We state and prove generalizations of the Differentiation Lemma and the Reynolds Transport Theorem in the general setting of smooth manifolds with corners (e.g. cuboids, spheres, $\mathbb{R}^n$, simplices). Several examples of manifolds with corners are ... More

Acylindrical actions for two-dimensional Artin groups of hyperbolic typeJun 07 2019For a two-dimensional Artin group $A$ whose associated Coxeter group is hyperbolic, we prove that the action of $A$ on the hyperbolic space obtained by coning off certain subcomplexes of its modified Deligne complex is acylindrical and universal. As a ... More

Invariant Schreier decorations of unimodular random networksJun 07 2019We prove that every $2d$-regular unimodular random network carries an invariant random Schreier decoration. Equivalently, it is the Schreier coset graph of an invariant random subgroup of the free group $F_d$. As a corollary we get that every $2d$-regular ... More

Congruences on Orthogonal Rook Monoids and Symplectic Rook MonoidsJun 07 2019We give a complete classification of all nonuniform congruences on orthogonal rook monoids and symplectic rook monoids. We find that there are four kinds of nonuniform congruences on the orthogonal rook monoids ${OR}_n$ for even $n\ne 4$, and we describe ... More

Sobolev spaces for multi-black hole initial dataJun 05 2019In this article we introduce weighted Sobolev spaces that are well suited to treat initial data for multiple black hole systems. We prove general results for elliptic operators on these spaces and give a simple proof of existence of a class of initial ... More

Green's relations and stability for subsemigroupsJun 05 2019We prove new results on inheritance of Green's relations by subsemigroups in the presence of stability of elements, and provide counterexamples in other cases to show in particular that in general right-stable semigroups cannot be embedded in left-stable ... More

Flexible stability and nonsoficityJun 05 2019A sofic group $G$ is said to be flexibly stable if every sofic approximation to $G$ can converted to a sequence of disjoint unions of Schreier graphs by modifying an asymptotically vanishing proportion of edges. We establish that if $\mathrm{PSL}_d(\mathbb{Z})$ ... More

Roads to topological censorshipJun 05 2019In this note we review some aspects of topological censorship. We present several (actually five) alternative sets of hypotheses which allow the proof of a topological censorship theorem for spacetimes with conformal completions at infinity and vanishing ... More

Partial actions and proper extensions of two-sided restriction semigroupsJun 05 2019We introduce and study several classes of partial actions of two-sided restriction semigroups that generalize partial actions of monoids and of inverse semigroups. We prove a structure result on proper extensions of two-sided restriction semigroups in ... More

Fixed subgroups and computation of auto-fixed closures in free-abelian times free groupsJun 05 2019The classical result by Dyer--Scott about fixed subgroups of finite order automorphisms of $F_n$ being free factors of $F_n$ is no longer true in $Z^m\times F_n$. Within this more general context, we prove a relaxed version in the spirit of Bestvina--Handel ... More

Degree 3 unramified cohomology of classifying spaces for exceptional groupsJun 05 2019Let $G$ be a reductive group defined over an algebraically closed field of characteristic $0$ such that the Dynkin diagram of $G$ is the disjoint union of diagrams of types $G_{2}, F_{4}, E_{6}, E_{7}, E_{8}$. We show that the degree $3$ unramified cohomology ... More

Estimates for matrix coefficients of representationsJun 05 2019Estimates for matrix coefficients of unitary representations of semisimple Lie groups have been studied for a long time, starting with the seminal work by Bargmann, by Ehrenpreis and Mautner, and by Kunze and Stein. Two types of estimates have been established: ... More

Non Commutative Algebraic Geometry I: Monomial Equations with a Single VariableJun 05 2019This paper is the first in a sequence on the structure of sets of solutions to systems of equations over a free associative algebra. We start by constructing a Makanin-Razborov diagram that encodes all the homogeneous solutions to a homogeneous system ... More

Formulating basic notions of finite group theory via the lifting propertyJun 05 2019We reformulate several basic notions of notions in finite group theory in terms of iterations of the lifting property (orthogonality) with respect to particular morphisms. Our examples include the notions being nilpotent, solvable, perfect, torsion-free; ... More

Conformal Geometry of Embedded Manifolds with Boundary from Universal Holographic FormulaeJun 04 2019For an embedded conformal hypersurface with boundary, we construct critical order local invariants and their canonically associated differential operators. These are obtained holographically in a construction that uses a singular Yamabe problem and a ... More

The ambiguity function and the displacement operator basis in quantum mechanicsJun 04 2019We present a method for calculating expectation values of operators in terms of a corresponding c-function formalism which is not the Wigner--Weyl position-momentum phase-space, but another space. Here, the quantity representing the quantum system is ... More

Affine Killing vector fields on homogeneous surfaces with torsionJun 04 2019Many extensions of General Relativity are based on considering metric and affine structures as independent properties of spacetime. This leads to the possibility of introducing torsion as an independent degree of freedom. In this article we examine the ... More

Global existence for systems of nonlinear wave equations with bounded, stable asymptotic systemsJun 04 2019Some systems of nonlinear wave equations admit global solutions for all sufficiently small initial data, while others do not. The (classical) null condition guarantees that such a result holds, but it is too strong to capture certain systems -- most famously ... More

Quasi-automatic groups are asynchronously automaticJun 04 2019A quasi-automatic semigroup is a finitely generated semigroup with a rational set of representatives such that the graph of right multiplication by any generator is a rational relation. A asynchronously automatic semigroup is a quasi-automatic semigroup ... More

Automorphism-invariant positive definite functions on free groupsJun 04 2019In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new perspectives and ... More

The Farrell--Jones Conjecture for normally poly-free groupsJun 04 2019We prove the $K$- and $L$-theoretic Farrell--Jones Conjecture with coefficients in an additive category for every normally poly-free group, in particular for even Artin groups of FC-type, and for all groups of the form $A\rtimes \mathbb{Z}$ where $A$ ... More

Connective Bieberbach groupsJun 03 2019We prove that a Bieberbach group with trivial center is not connective and use this property to show that a Bieberbach group is connective if and only if it is poly-Z.

A $2$-compact group as a spetsJun 03 2019Jun 12 2019In 1998 Malle introduced spetses which are mysterious objects with non-real Weyl groups. In algebraic topology, a $p$-compact group $\mathbf{X}$ is a space which is a homotopy-theoretic $p$-local analogue of a compact Lie group. A connected $p$-compact ... More

A $2$-compact group as a spetsJun 03 2019In 1999 Brou\'{e}, Malle and Michel introduced the concept of a ``spets'' which is a mysterious object with a non-real Weyl group. In algebraic topology, a $p$-compact group $X$ is a space which is a homotopy-theoretic $p$-local analogue of a compact ... More

Linear stability of slowly rotating Kerr black holesJun 03 2019We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equation: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure gauge term. We work in ... More

Alternating quotients of RACGJun 03 2019Let $W$ be a right-angled Coxeter group corresponding to a finite non-discrete graph $\mathcal{G}$. Our main theorem says that $\mathcal{G}^c$ is connected if and only if for any infinite index quasiconvex subgroup $H$ of $W$ and any finite subset $\{ ... More

The role of pseudo-hypersurfaces in non-holonomic motionJun 03 2019The geometry of hypersurfaces is generalized to pseudo-hypersurfaces, which are defined by Pfaff equations. The general methods are then applied to modeling the kinematics of motion constrained by a single linear, non-holonomic constraint. They are then ... More

On Derrick's theorem in curved spacetimeJun 03 2019We extend Derrick's theorem to the case of a generic irrotational curved spacetime adopting a strategy similar to the original proof. We show that a static relativistic star made of real scalar fields is never possible regardless of the geometrical properties ... More

The strategy of pattern recognition via Artin transfers applied to finite towers of 2-class fieldsJun 02 2019The isomorphism type of the Galois group of the 2-class field tower of quadratic number fields having a 2-class group with abelian type invariants (4,4) is determined by means of information on the transfer of 2-classes to unramified abelian 2-extensions, ... More

The Einstein-Infeld-Hoffmann legacy in mathematical relativity. Part I: The classical motion of charged point particlesJun 01 2019Einstein, Infeld, and Hoffmann (EIH) claimed that the field equations of general relativity theory alone imply the equations of motion of neutral matter particles, viewed as point singularities in space-like slices of spacetime; they also claimed that ... More

The Einstein-Infeld-Hoffmann legacy in mathematical relativity. Part I: The classical motion of charged point particlesJun 01 2019Jun 10 2019Einstein, Infeld, and Hoffmann (EIH) claimed that the field equations of general relativity theory alone imply the equations of motion of neutral matter particles, viewed as point singularities in space-like slices of spacetime; they also claimed that ... More

Fundamental groups of split real Kac-Moody groups and generalized real flag manifoldsMay 31 2019We determine the fundamental groups of algebraically simply connected split real Kac-Moody groups endowed with the Kac-Peterson topology. In analogy to the finite-dimensional situation, the Iwasawa decomposition $G = KAU_+$ is a homeomorphism so that ... More

Formal language convexity in left-orderable groupsMay 30 2019We propose a criterion for the regularity of a formal language representation when passing to subgroups. We use this criterion to show that the regularity of a positive cone language in a left-orderable group passes to its finite index subgroups, and ... More

Noether Converse: all identically conserved geometric tensors are metric variations of an action in (at least) D = 2May 30 2019The title's century-old conjecture is established fpr D=2 and is likely for all D.

The enumeration of coverings of closed orientable Euclidean manifolds $G_3$ and $G_5$May 29 2019There are only 10 Euclidean forms, that is flat closed three dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of $n$-fold coverings over orientable Euclidean manifolds $\mathcal{G}_{3}$ ... More

Which group algebras cannot be made zero by imposing a single non-monomial relation?May 29 2019For which groups $G$ is it true that for all fields $k$, every non-monomial element of the group algebra $k\,G$ generates a <i>proper</i> $2$-sided ideal? The only groups for which we know this are the torsion-free abelian groups. We would like to know ... More

On the lattice of subgroups of a free group: complements and rankMay 29 2019A $\vee$-complement of a subgroup $H \leqslant \mathbb{F}_n$ is a subgroup $K \leqslant \mathbb{F}_n$ such that $H \vee K = \mathbb{F}_n$. If we also ask $K$ to have trivial intersection with $H$, then we say that $K$ is a $\oplus$-complement of $H$. ... More

Big mapping class groups acting on homologyMay 29 2019We study the action of (big) mapping class groups on the first homology of the corresponding surface. We give a precise characterization of the image of the induced homology representation.

From Hierarchical to Relative HyperbolicityMay 29 2019We provide a simple, combinatorial criteria for a hierarchically hyperbolic space to be relatively hyperbolic by proving a new formulation of relative hyperbolicity in terms of hierarchy structures. In the case of clean hierarchically hyperbolic groups, ... More

Exponent of Self-similar finite $p$-groupsMay 29 2019Let $p$ be a prime and $G$ a pro-$p$ group of finite rank that admits a faithful, self-similar action on the $p$-ary rooted tree. We prove that if the set $\{g\in G \ | \ g^{p^n}=1\}$ is a nontrivial subgroup for some $n$, then $G$ is a finite $p$-group ... More

The $κ$-(A)dS noncommutative spacetimeMay 29 2019The (3+1)-dimensional $\kappa$-(A)dS noncommutative spacetime is explicitly constructed by quantizing its semiclassical counterpart, which is the $\kappa$-(A)dS Poisson homogeneous space. Under minimal physical assumptions, it is explicitly proven that ... More

Sums of element orders in groups of odd orderMay 29 2019Denote by $G$ a finite group and by $\psi(G)$ the sum of element orders in $G$. If $t$ is a positive integer, denote by $C_t$ the cyclic group of order $t$ and write $\psi(t)=\psi(C_t)$. In this paper we proved the following Theorem A: Let $G$ be a non-cyclic ... More

Integrating Factors for Dirac-Schrodinger Operators: Improving Eigenvalue Estimates and Applications to Charged Positive Mass Theorems Outside Horizon(s)May 29 2019Let $(M^{n}, g)$ denote a Riemannian spin manifold of dimension $n$ with Dirac operator $D$ induced from the Levi-Cevita connection acing on the spinor bundle, $S$ ($D$ is also called the Atiyah-Singer Operator). Let $c: Cl(TM^{n}) \rightarrow End(S)$ ... More

On CW-complexes over groups with periodic cohomologyMay 28 2019If $G$ has $4$-periodic cohomology and at most two one-dimensional quaternionic representations, then $G$ has the D2 property if and only if $G$ has a balanced presentation. We use this to solve Wall's D2 problem for several infinite families of non-abelian ... More

On the Gelfand property for complex symmetric pairsMay 28 2019We first prove, for pairs consisting of a simply connected complex reductive group together with a connected subgroup, the equivalence between two different notions of Gelfand pairs. This partially answers a question posed by Gross, and allows us to use ... More

Additive Conjugacy and the Bohr Compactification of Orthogonal RepresentationsMay 28 2019We say that two unitary or orthogonal representations of a finitely generated group $G$ are {\em additive conjugates} if they are intertwined by an additive map, which need not be continuous. We associate to each representation of $G$ a topological action ... More

A Geometric Characterization of Rational GroupsMay 27 2019We give a geometric characterization of finite rational groups. In particular, we prove that a finite group is rational if and only if there exists a finite geometry $\Gamma$ of type $I$ and action of $G$ on $\Gamma$ as a group of automorphisms such that ... More

Bianchi models with a free massless scalar field: invariant sets and higher symmetriesMay 27 2019We scrutinize the overall structure of the space of cosmological models of Bianchi type I-VII$_h$ that contain a free massless scalar field, with a spatially homogeneous gradient $\nabla_\mu \varphi$ that generally breaks isotropy, in addition to a standard ... More

Symmetries of complex flat manifoldsMay 27 2019In this article we show how to calculate the group of automorphisms of the flat K\"ahler manifolds. Moreover we are interested in the problem of classification such manifolds up to biholomorphism. We consider these problems from two points of view. The ... More

Benchmark of Polygon Quality Metrics for Polytopal Element MethodsMay 27 2019Polytopal Element Methods (PEM) allow to solve differential equations on general polygonal and polyhedral grids, potentially offering great flexibility to mesh generation algorithms. Differently from classical finite element methods, where the relation ... More

On the number of irreducible real-valued characters of a finite groupMay 26 2019We prove that there exists an integer-valued function f on positive integers such that if a finite group G has at most k real-valued irreducible characters, then |G/Sol(G)| is at most f(k), where Sol(G) denotes the largest solvable normal subgroup of ... More

On the minimum degree of the power graph of a finite cyclic groupMay 26 2019The power graph $\mathcal{P}(G)$ of a finite group $G$ is the simple undirected graph whose vertex set is $G$, in which two distinct vertices are adjacent if one of them is an integral power of the other. For an integer $n\geq 2$, let $C_n$ denote the ... More

The semigroup of star partial homeomorphisms of a finite deminsional Euclidean spaceMay 26 2019In the paper the notion of a star partial homeomorphism of a finite dimensional Euclidean space $\mathbb{R}^n$ is introduced. We describe the structure of the semigroup $\mathbf{PStH}_{\mathbb{R}^n}$ of star partial homeomorphisms of the space $\mathbb{R}^n.$ ... More

On Free Polyadic GroupsMay 25 2019In this article, for a polyadic group(G,f),derived from group G by automorphism G and element b, we give a necessary and sufficient condition in terms of the group, the automorphism G, and the element b, in order that the polyadic group becomes free.

Abelian subgroups, nilpotent subgroups, and the largest character degree of a finite groupMay 25 2019Let $H$ be an abelian subgroup of a finite group $G$ and $\pi$ the set of prime divisors of $|H|$. We prove that $|H O_{\pi}(G)/ O_{\pi}(G)|$ is bounded above by the largest character degree of $G$. A similar result is obtained when $H$ is nilpotent.

Recognizing pro-R closures of regular languagesMay 24 2019Given a regular language L, we effectively construct a unary semigroup that recognizes the topological closure of L in the free unary semigroup relative to the variety of unary semigroups generated by the pseudovariety R of all finite R-trivial semigroups. ... More

Taylor expansions of groups and filtered-formalityMay 24 2019Let $G$ be a finitely generated group, and let $\Bbbk{G}$ be its group algebra over a field of characteristic $0$. A Taylor expansion is a certain type of map from $G$ to the degree completion of the associated graded algebra of $\Bbbk{G}$ which generalizes ... More

Leibniz A-algebrasMay 24 2019A finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually ... More

Leibniz A-algebrasMay 24 2019Jun 03 2019A finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually ... More

Finite non-cyclic $p$-groups whose number of subgroups is minimalMay 24 2019Recent results of Qu and Tuarnauceanu describe explicitly the finite p-groups which are not elementary abelian and have the property that the number of their subgroups is maximal among p-groups of a given order. We complement these results from the bottom ... More

Convergence towards the end space for random walks on Schreier graphsMay 24 2019We consider a transitive action of a finitely generated group $G$ and the Schreier graph $\Gamma$ it defines. For a probability measure $\mu$ on $G$ with a finite first moment we show that if the induced random walk is transient, it converges towards ... More

The Baum-Connes conjecture: an extended surveyMay 24 2019We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.

Parallel Coordinate Order for High-Dimensional DataMay 24 2019Visualization of high-dimensional data is counter-intuitive using conventional graphs. Parallel coordinates are proposed as an alternative to explore multivariate data more effectively. However, it is difficult to extract relevant information through ... More

On the entropies of subshifts of finite type on countable amenable groupsMay 24 2019Let $G,H$ be two countable amenable groups. We introduce the notion of group charts, which gives us a tool to embed an arbitrary $H$-subshift into a $G$-subshift. Using an entropy addition formula derived from this formalism we prove that whenever $H$ ... More

Polynomial-time proofs that groups are hyperbolicMay 23 2019It is undecidable in general whether a given finitely presented group is word hyperbolic. We use the concept of pregroups, introduced by Stallings, to define a new class of van Kampen diagrams, which represent groups as quotients of virtually free groups. ... More

Escaping a neighborhood along a prescribed sequence in Lie groups and Banach algebrasMay 23 2019It is shown that Jamison sequences, introduced in [C. Badea and S. Grivaux, Unimodular eigenvalues, uniformly distributed sequences and linear dynamics, Adv. Math. 211 (2007), no. 2, 766--793], arise naturally in the study of topological groups with no ... More