Related papers: Groups with fast-growing conjugator length functio…

We construct a finitely presented group $G$ with non-quadratic Dehn function $f$ majorizable by a quadratic function on arbitrary long intervals.

We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the…

In recent work, Bacher and de la Harpe define and study conjugacy growth series for finitary permutation groups. In two subsequent papers, Cotron, Dicks, and Fleming study the congruence properties of some of these series. We define a new…

We construct a 2-generator recursively presented group with infinite torsion length. We also explore the construction in the context of solvable and word-hyperbolic groups.

We continue the investigation, that began in [3] and [4], into finite groups whose set of nontrivial conjugacy class sizes form an arithmetic progression. Let $G$ be a finite group and denote the set of conjugacy class sizes of $G$ by ${\rm…

We study completions of the group algebra of a finitely generated group and relate nuclearity of such a completion to growth properties of the group. This extends previous work of Jolissaint on nuclearity of rapidly decreasing functions on…

We study a function $\mathcal{L}_{\Gamma}$ which quantifies the LEF (local embeddability into finite groups) property for a finitely generated group $\Gamma$. We compute this "LEF growth" function in some examples, including certain wreath…

We prove that a finitely generated solvable group which is not virtually nilpotent has exponential conjugacy growth.

For a residually finite group $G$, its normal subgroups $G\supset G_1\supset G_2\cdots$ with $\cap_{n\in\mathbb N}G_n=\{e\}$ and for a growth function $\gamma$ we construct a unitary representation $\pi_\gamma$ of $G$. For the minimal…

Let G be a finitely presented group, and let {G_i} be a collection of finite index normal subgroups that is closed under intersections. Then, we prove that at least one of the following must hold: 1. G_i is an amalgamated free product or…

In this work we study the structure of finitely generated groups for which a space of harmonic functions with fixed polynomial growth is finite dimensional. It is conjectured that such groups must be virtually nilpotent (the converse…

Given a group $G$ and elements $x_1,x_2,\dots, x_\ell\in G$, the commutator of the form $[x_1,x_2,\dots, x_\ell]$ is called a commutator of length $\ell$. The present paper deals with groups having only finitely many commutators of length…

Every countable group that does not contain a finitely generated subgroup of exponential growth imbeds in a finitely generated group of subexponential growth. This produces in particular the first examples of groups of subexponential growth…

In [K. Bou-Rabee, B. Seward, J. Reine Angwe. Math. 2016] Bou-Rabee and Seward constructed examples of finitely generated residually finite groups $G$ whose residual finiteness growth function $\mathcal{F}_G$ can be at least as fast as any…

For a finitely generated lawless group $\Gamma$ and $n \in \mathbb{N}$, let $\mathcal{A}_{\Gamma} (n)$ be the minimal positive integer $M_n$ such that for all nontrivial reduced words $w$ of length at most $n$ in the free group of fixed…

We construct the first example of a finitely-presented, residually-finite group that contains an infinite sequence of non-isomorphic finitely-presented subgroups such that each of the inclusion maps induces an isomorphism of profinite…

We say that a finitely generated group $\Gamma$ is self-simulable if every effectively closed action of $\Gamma$ on a closed subset of $\{\texttt{0},\texttt{1}\}^{\mathbb{N}}$ is the topological factor of a $\Gamma$-subshift of finite type.…

We prove the exponential growth of product replacement graphs for a large class of groups. Much of our effort is dedicated to the study of product replacement graphs of Grigorchuk groups, where the problem is most difficult.

This paper studies the locally uniform exponential growth and product set growth for a finitely generated group $G$ acting properly on a finite product of hyperbolic spaces. Under the assumption of coarsely dense orbits or shadowing…

We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.