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

In this article, we study the asymptotic behaviour of conjugacy separability for wreath products of abelian groups. We fully characterise the asymptotic class in the case of lamplighter groups and give exponential upper and lower bounds for…

We define and study a notion of free wreath product with amalgamation for compact quantum groups. These objects were already introduced in the case of duals of discrete groups under the name "free wreath products of pairs" in a previous…

We study the unit group of the modular group algebra KG, where G is a 2-group of maximal class. We prove that the unit group of KG possesses a section isomorphic to the wreath product of a group of order two with the commutator subgroup of…

We consider the group property of being icc. We give several examples of icc groups and study its stability under usual algebraic constructions.

We examine the conjugacy growth series of all wreath products of the finitary permutation groups $\text{Sym}(X)$ and $\text{Alt}(X)$ for an infinite set $X$. We determine their asymptotics, and we characterize the limiting behavior between…

For a class of wreath-like product groups with property (T), we describe explicitly all the embeddings between their von Neumann algebras. This allows us to provide a continuum of ICC groups with property (T) whose von Neumann algebras are…

We describe an effective version of the conjugacy problem and study it for wreath products and free solvable groups. The problem involves estimating the length of short conjugators between two elements of the group, a notion which leads to…

We introduce a new class of groups called wreath-like products. These groups are close relatives of the classical wreath products and arise naturally in the context of group theoretic Dehn filling. Unlike ordinary wreath products, many…

We show that an accessible group with infinitely many ends has property $R_{\infty}$. That is, it has infinitely many twisted conjugacy classes for any twisting automorphism. We deduce that having property $R_{\infty}$ is undecidable…

Let $H$ be an extension of a finite group $Q$ by a finite group $G$. Inspired by the results of duality theorems for \'etale gerbes on orbifolds, we describe the number of conjugacy classes of $H$ that maps to the same conjugacy class of…

We present a survey of our recent research on varieties, generated by wreath products of groups. In particular, the full classification of all cases, when the (cartesian or direct) wreath product of any abelian groups $A$ and $B$ generates…

Let $G$ be a finite group with $k$ conjugacy classes, and $S(\infty)$ be the infinite symmetric group, i.e. the group of finite permutations of $\left\{1,2,3,\ldots\right\}$. Then the wreath product $G_{\infty}=G\sim S(\infty)$ of $G$ with…

The irreducible spin character values of the wreath products of the hyperoctahedral groups with an arbitrary finite group are determined.

Many results have been established that show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper is to show several results about solvability concerning 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…

Normal subgroups and there properties for finite and infinite iterated wreath products $S_{n_1}\wr \ldots \wr S_{n_m}$, $n, m \in \mathbb{N}$ are founded. The special classes of normal subgroups and there orders are investigated. Special…

We provide a necessary and sufficient condition for the restricted wreath product $A\wr B$ to be $\mathcal{C}$-hereditarily conjugacy separable where $\mathcal{C}$ is an extension-closed pseudovariety of finite groups. Moreover, we prove…

In the note some construction of Lie algebras is introduced. It is proved that the construction has the same property as a well known wreath product of groups [1]: Any extension of groups can be embedded into their wreath product [2].

For the finite groups GU(3), SU(3), GL(3), SL(3) over a finite field we solve the class product problem, i.e., we give a complete list of $m$-tuples of conjugacy classes whose product does not contain the identity matrix.

Inspired by the definition of generalized wreath product of permutation groups, we define the generalized wreath product of graphs, containing the classical Cartesian and wreath product of graphs as particular cases. We prove that the…