Related papers: Almost Representations and Asymptotic Representati…

We say that a finite group $G$ satisfies the independence property if, for every pair of distinct elements $x$ and $y$ of $G$, either $\{x,y\}$ is contained in a minimal generating set for $G$ or one of $x$ and $y$ is a power of the other.…

Let $G$ be a residually finite group. We give an explicit example in the discrete Heisenberg group that the Brown measure of multiplication operators $A \in \mathbb{Z}[G] \subseteq \mathcal{B}(\ell^2(G))$ in general can not be approximated…

Self-similar groups provide a rich source of groups with interesting properties; e.g., infinite torsion groups (Burnside groups) and groups with an intermediate word growth. Various self-similar groups can be described by a recursive…

We introduce the property of having good subgroups for actions of countable discrete groups on compact metrizable spaces, and show that it implies comparison when the acting group is amenable. As a consequence, free actions on…

In his volume [5] on "Symmetry Breaking for Compact Lie Groups" Mike Field quotes a private communication by Jorge Ize claiming that any bifurcation problem with absolutely irreducible group action would lead to bifurcation of steady…

Discrete groups are widely used in the expression of flavor symmetries of leptons. In this paper, we employ a novel mathematical object called group-algebra (GA) to describe symmetries of the leptonic mass matrices. A GA element is…

We exhibit infinitely many pairs of non-isomorphic finitely presented, residually finite groups $\Delta$ and $\Gamma$ with $\Delta$ having Property FA, $\Gamma$ having a non-trivial action on a tree and $\Delta$ and $\Gamma$ having…

The tempered spectrum of the similitude groups of non-degenerate symplectic, hermitian, or split orthogonal forms defined over $p$\snug-adic groups of characteristic zero is studied. The components of representations induced from discrete…

For a finite group $G$, the representation dimension is the smallest integer realizable as the degree of a complex faithful representation of $G$. In this article, we compute representation dimension for some $p$-groups, their direct…

This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…

We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…

We introduce a notion of a group-partition for a finite Abelian group, which is a generalized notion of the standard partition. To obtain asymptoticdistributions of group-partition, we study the Dirichlet series for group-partitions by…

In this article we study asymptotic properties of certain discrete groups $\Gamma$ acting by isometries on a product $\XX=\XX_1\times \XX_2$ of locally compact Hadamard spaces. The motivation comes from the fact that Kac-Moody groups over…

A topological group $G$ has the Approximate Fixed Point (AFP) property on a bounded convex subset $C$ of a locally convex space if every continuous affine action of $G$ on $C$ admits a net $(x_i)$, $x_i\in C$, such that…

For numerical semigroups with a specified list of (not necessarily minimal) generators, we obtain explicit asymptotic expressions, and in some cases quasipolynomial/quasirational representations, for all major factorization length…

We define the scattered subsets of a group as asymptotic counterparts of scattered subspaces of a topological space, and prove that a subset $A$ of a group $G$ is scattered if and only if $A$ contains no piecewise shifted $IP$-subsets. For…

Let K be a number field and let A be its ring of integers. Let G be a connected, noncommutative, absolutely almost simple algebraic K-group. If the K-rank of G equals 2, then G(A[t]) is not finitely presented.

For a group $G$, we denote by $\stackrel{\leftrightarrow}{G}$ the coarse space on $G$ endowed with the coarse structure with the base $\{\{ (x,y)\in G\times G: y\in x^F \} : F \in [G]^{<\omega} \}$, $x^F = \{z^{-1} xz : z\in F \}$. Our goal…

We describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups admitting an infinite minimal presentation. We…

We prove that every finitely generated, residually finite group $G$ embeds into a finitely generated perfect branch group $\Gamma$ such that many properties of $G$ are preserved under this embedding. Among those are the properties of being…