Related papers: On approximation properties of semidirect products…

In this article, we prove that a semidirect product of a locally finite group with a surjunctive group is also surjunctive. We also prove that a surjunctive-by-locally finite group is again surjunctive.

We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible…

Let $\mathbb{Z}$ be the additive (semi)group of integers. We prove that for a finite semigroup $S$ the direct product $\mathbb{Z}\times S$ contains only countably many subdirect products (up to isomorphism) if and only if $S$ is regular. As…

If G is a semidirect product N by H with N normal and finitely generated then G has the property that every finite group is a quotient of some finite index subgroup of G if and only if one of N and H has this property. This has applications…

We study conditions under which subdirect products of various types of algebraic structures are finitely generated or finitely presented. In the case of two factors, we prove general results for arbitrary congruence permutable varieties,…

We establish a general criterion for the finite presentability of subdirect products of groups and use this to characterize finitely presented residually free groups. We prove that, for all $n\in\mathbb{N}$, a residually free group is of…

The residual closure of a subgroup $H$ of a group $G$ is the intersection of all virtually normal subgroups of $G$ containing $H$. We show that if $G$ is generated by finitely many cosets of $H$ and if $H$ is commensurated, then the…

Hard to summarize concisely; here are the high points. The first two statements below are ring-theoretic; in these R is a nontrivial ring, R^\omega, and \bigoplus_\omega R are the direct product, respectively direct sum, of countably many…

We investigate the structure of subdirect products of groups, particularly their finiteness properties. We pay special attention to the subdirect products of free groups, surface groups and HNN extensions. We prove that a finitely presented…

In various classes of infinite groups, we identify groups that are presentable by products, i.e. groups having finite index subgroups which are quotients of products of two commuting infinite subgroups. The classes we discuss here include…

Groups that can be approximated by finite groups have been the center of much research. This has led to the investigations of the subgroups of metric ultraproducts of finite groups. This paper attempts to study the dual problem: what are…

We prove that there exist finitely presented, residually finite groups that are profinitely rigid in the class of all finitely presented groups but not in the class of all finitely generated groups. These groups are of the form $\Gamma…

In this paper we prove two new results about closed semigroups in the family of solvable groups H_{mn} that are semidirect products of R^m and R^n, and for which the structure homomorphism maps nontrivially into the center of Aut(R^n). The…

We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional…

We prove that for any finitely generated group $G$ and any $k\geq1$, the space of $k$-colorings of $G$ does not admit a strict self-embedding. This settles the Gottschalk surjunctivity conjecture and, consequently, Kaplansky's direct…

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…

In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…

We construct a finitely generated residually finite group $G$ with the property that every finite index subgroup of $G$ contains a subgroup isomorphic to Promislow's group. Hence $G$ does not have a finite index subgroup with the unique…

We prove two results. (1) There is an absolute constant $D$ such that for any finite quasisimple group $S$, given 2D arbitrary automorphisms of $S$, every element of $S$ is equal to a product of $D$ `twisted commutators' defined by the…

Bestvina's notion of a Z-structure provides a general framework for group boundaries that includes Gromov boundaries of hyperbolic groups and visual boundaries of CAT(0) groups as special cases. A refinement, known as an EZ-structure has…