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

We consider the finitely generated groups acting on a regular tree with almost prescribed local action. We show that these groups embed as cocompact irreducible lattices in some locally compact wreath products. This provides examples of…

We show that amenability, the Haagerup property, the Kazhdan's property (T) and exactness are preserved under taking second nilpotent product of groups. We also define the restricted second nilpotent wreath product of groups, this is a…

Let $G$ be a finite group. K. Harada conjectured that the product of degrees of all irreducible characters of $G$ divides the product of lengths of all conjugacy classes of $G$. We verify this conjecture for finite general linear groups and…

Reidemeister (or twisted conjugacy) classes are considered in restricted wreath products of the form $G\wr \mathbb{Z}^k$, where $G$ is a finite group. For an automorphism $\varphi$ of finite order (supposed to be the same for the torsion…

We prove necessary and sufficient conditions for when graph wreath products are residually finite, generalising known results for the permutational wreath product and free product cases.

A new general formula for the number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.

Generalizing results of Higman and Houghton on varieties generated by wreath products of finite cycles, we prove that the (direct or cartesian) wreath product of arbitrary abelian groups $A$ and $B$ generates the product variety $var (A)…

We classify certain cases when the wreath products of distinct pairs of groups generate the same variety. This allows us to investigate the subvarieties of some nilpotent-by-abelian product varieties ${\mathfrak U}{\mathfrak V}$ with the…

In this article, some necessary conditions of group vertex magicness of graphs with at least one pendant, group vertex magicness of product graphs, are proved. A characterization of group vertex magicness of trees of diameter up to 5. for…

This note presents the study of the conjugacy classes of elements of some given finite order n in the Cremona group of the plane. In particular, it is shown that the number of conjugacy classes is infinite if n is even, n=3 or n=5, and that…

In this paper we classify the finite groups satisfying the following property $P_4$: their orders of representatives are set-wise relatively prime for any 4 distinct non-central conjugacy classes.

We construct a hyperbolic group with a finitely presented subgroup, which has infinitely many conjugacy classes of finite-order elements. We also use a version of Morse theory with high dimensional horizontal cells and use handle…

Starting with group graded Morita equivalences, we obtain Morita equivalences for tensor products and wreath products.

An infinitary version of braid groups has been considered as a direct limit of n-braid groups. However, we can imagine more complicated braids with infinitely many strings. We invetisgate basic properties especially when the number of…

Using 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…

Given sofic approximations for countable, discrete groups $G,H$, we construct a sofic approximation for their wreath product $G\wr H$.

Motivated by computational efficiency in algebraic automata theory here we define the cascade product of permutation groups as an external product, as a generic extension. It is the most general hierarchical product that uses arbitrary…

We extend work of the first author and Khoussainov to show that being Cayley automatic is closed under taking the restricted wreath product with a virtually infinite cyclic group. This adds to the list of known examples of Cayley automatic…

We characterize which permutational wreath products W^(X)\rtimes G are finitely presented. This occurs if and only if G and W are finitely presented, G acts on X with finitely generated stabilizers, and with finitely many orbits on the…

We prove, for various important classes of Mealy automata, that almost all generated groups have an element of infinite order. In certain cases, it also implies other results such as exponential growth.