Related papers: On Tame Subgroups of Finitely Presented Groups

We extend the notion of a tame covering of a pair (X,D) where X is a regular scheme and D is a normal crossing divisor (cf. SGA1), to pairs (X,Y) where X is an arbitrary scheme and Y is a closed subset in X. We show that the abelianized…

It has been shown that for every prime number $p$, the pseudovariety $\mathsf{G}_p$ of all finite $p$-groups is tame with respect to an implicit signature containing the canonical implicit signature. In this paper, we generalize this result…

Let $\mathcal G$ denote the space of finitely generated marked groups. For any finitely generated group $G$, we construct a continuous, injective map $f$ from the space of subgroups $Sub(G)$ to $\mathcal G$ that sends conjugate subgroups to…

We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.

We describe the endomorphisms of the direct product of two free groups of finite rank and obtain conditions for which the subgroup of fixed points is finitely generated and we do the same for periodic points. We also describe the…

Answering a question of Dan Haran and generalizing some results of Aschbacher-Guralnick and Suzuki, we prove that given a set of primes pi, any finite group can be generated by a pi-subgroup and a pi'-subgroup. This gives a free product…

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…

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 construct explicitly a family of proper subgroups of the tame automorphism group of affine three-space (in any characteristic) which are generated by the affine subgroup and a non-affine tame automorphism. One important corollary is the…

We show that for any pair of non-trivial finite groups, their coproduct in the category of finite groups is not representable.

We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.

We prove that in every finitely generated profinite group, every subgroup of finite index is open; this implies that the topology on such groups is determined by the algebraic structure. This is deduced from the main result about finite…

It is proven that if a finitely presented group is one ended it has asymptotic dimension bigger than one. It follows that finitely presented groups with asdim 1 are virtually free. A counterexample is given for the finitely generated case.

The study of localizations of groups has concentrated on group theoretic properties which are preserved by localization. In this paper we look at finitely generated soluble groups and determine when the local groups associated with them are…

We give a survey on results regarding self-similar and automaton presentations of free groups and semigroups and related products. Furthermore, we discuss open problems and results with respect to algebraic decision problems in this area.

In one of our previous articles, we outlined the formulation of a version of the categorical arithmetic local Langlands conjecture. The aims of this article are threefold. First, we provide a detailed account of one component of this…

Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.

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 show that the product of two partial normal subgroups of a locality (in the sense of Chermak) is again a partial normal subgroup. This generalizes a theorem of Chermak and fits into the context of building a local theory of localities.

We examine the question of which finitely generated groups act properly on a finite product of locally finite simplicial trees and present evidence in favour of hyperbolic surface groups having such an action. We also give a completely…