Related papers: On Tame Subgroups of Finitely Presented Groups

Given a finitely generated linear group $G$ over $\mathbb{Q}$, we construct a simple group $\Gamma$ that has the same finiteness properties as $G$ and admits $G$ as a quasi-retract. As an application, we construct a simple group of type…

Let G be any locally compact, unimodular, metrizable group. The main result of this paper, roughly stated, is that if F<G is any finitely generated free group and \Gamma < G any lattice, then up to a small perturbation and passing to a…

We prove that there is a second countable locally compact group that does not embed as a closed subgroup in any compactly generated locally compact group, and discuss various related embedding and non-embedding results.

We give new and improved results on the freeness of subgroups of free profinite groups: A subgroup containing the normal closure of a finite word in the elements of a basis is free; Every infinite index subgroup of a finitely generated…

In the paper it is proven that Carter subgroups of a finite group are conjugate. A complete classification of Carter subgroups in finite almost simple groups is also obtained.

In representation theory, the problem of classifying pairs of matrices up to simultaneous similarity is used as a measure of complexity; classification problems containing it are called wild problems, and the other are referred to as tame.

We prove that Thompson's group $F$ has a subgroup $H$ such that the conjugacy problem in $H$ is undecidable and the membership problem in $H$ is easily decidable. The subgroup $H$ of $F$ is a closed subgroup of $F$. That is, every function…

Given nontrivial finite groups $A$ and $B$, not both of order 2, we prove that every finite simple group of sufficiently large rank is an image of the free product $A \ast B$. To show this, we prove that every finite simple group of…

For a subgroup of a free product of finite groups, we obtain necessary conditions (on its Kurosh decomposition) to be verbally closed.

We study actions of linear algebraic groups on finite-dimensional central simple algebras. We describe the fixed algebra for a broad class of such actions.

In this paper we consider the {\em conjugacy stability} property of subgroups and provide effective procedures to solve the problem in several classes of groups. In particular, we start with free groups, that is, we give an effective…

In this note we prove the following results: $\bullet$ If a finitely presented group $G$ admits a strongly aperiodic SFT, then $G$ has decidable word problem. More generally, for f.g. groups that are not recursively presented, there exists…

The class of refinement monoids (abelian monoids satisfying the Riesz refinement property) is subdivided into those which are tame, defined as being an inductive limit of finitely generated refinement monoids, and those which are wild,…

We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group G, we show that a finite subset X with |X X \^{-1} X |/ |X| bounded is…

We offer a direct proof of an elementary result concerning cohomological periods. As a corollary we show that given a finitely generated stably free resolution of Z over a finite group, two of its modules are free.

We prove that every verbally closed two-generated subgroup of a free solvable group G of a finite rank is a retract of G.

We prove that if a totally disconnected locally compact group admits a topologically free boundary, then the reduced crossed product of continuous functions on its Furstenberg boundary by the group is simple. We also prove a partial…

We exhibit classes of groups in which the word problem is uniformly solvable but in which there is no algorithm that can compute finite presentations for finitely presentable subgroups. Direct products of hyperbolic groups, groups of…

Let $G$ be a finitely generated group. We prove that the $n$-fold tensor product $G^{\otimes n}$ is finite (resp. polycyclic) if and only $G$ is finite (resp. polycyclic). Further, assuming that $G$ is finitely presented, we show that…

Recent results on finite open group transformations are reviewed.