Related papers: Wreath product of groups with infinite conjugacy c…

We show that the wreath product $G \wr \mathbb{Z}^n$ of any finitely generated group $G$ with $\mathbb{Z}^n$ has finite palindromic width. We also show that $C \wr A$ has finite palindromic width if $C$ has finite commutator width and $A$…

We study the preservation of certain properties under products of classes of finite structures. In particular, we examine indivisibility, definable self-similarity, the amalgamation property, and the disjoint n-amalgamation property. We…

This is a survey of way that the sizes of conjugacy classes influence the structure of finite groups

We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of…

Let $G$ be a finite group. An element $g$ of $G$ is called a vanishing element if there exists an irreducible character $\chi$ of $G$ such that $\chi(g) = 0$; in this case, we say that the conjugacy class of $g$ is a vanishing conjugacy…

It is shown that membership in rational subsets of wreath products H \wr V with H a finite group and V a virtually free group is decidable. On the other hand, it is shown that there exists a fixed finitely generated submonoid in the wreath…

We study the second bounded cohomology of an amalgamated free product of groups, and an HNN extension of a group. As an application, we have a group with infinitely many ends has infinite dimensional second bounded cohomology.

It is known that the notion of a transitive subgroup of a permutation group $P$ extends naturally to the subsets of $P$. We study transitive subsets of the wreath product $G \wr S_n$, where $G$ is a finite abelian group. This includes the…

In this short note, we classify pairs of conjugacy classes of the symmetric group such that any non-linear irreducible character of the symmetric group vanishes on at least one of them.

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 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 study twisted conjugacy classes of a family of groups which are called Houghton's groups $\mathcal{H}_n$ ($n \in\mathbb{N}$), the group of translations of $n$ rays of discrete points at infinity. We prove that the Houghton's groups…

Recently, the authors gave some conditions under which a direct product of finitely many groups is $\mathcal{V}-$capable if and only if each of its factors is $\mathcal{V}-$capable for some varieties $\mathcal{V}$. In this paper, we extend…

We prove that if a Cartesian product of alternating groups is topologically finitely generated, then it is the profinite completion of a finitely generated residually finite group. The same holds for Cartesian producs of other simple groups…

We study some infinite products of absolute zeta functions. Especially, we consider the convergence and the rationality of them.

A braided fusion category is said to have Property $\textbf{F}$ if the associated braid group representations factor over a finite group. We verify integral metaplectic modular categories have property $\textbf{F}$ by showing these…

Finitely generated (non-abelian) free metabelian pro-p groups, and wreath products of f.g. free abelian pro-p groups, are all finitely axiomatizable in the class of all profinite groups.

The conjugacy growth function counts the number of distinct conjugacy classes in a ball of radius $n$. We give a lower bound for the conjugacy growth of certain branch groups, among them the Grigorchuk group. This bound is a function of…

In this paper we study conjugacy separability of subdirect products of two free (or hyperbolic) groups. We establish necessary and sufficient criteria and apply them to fibre products to produce a finitely presented group $G_1$ in which all…

We give a partial solution a question of Grigorchuk, Nekrashevych, Sushchanskii and \v{S}uni\'k by giving an algorithm to test whether a finite state element of an infinite iterated (permutational) wreath product $\hat G = \mathbb…