Related papers: On accessibility of finitely generated groups

The girth of a finitely generated group G is the supremum of the girth of Cayley graphs for G over all finite generating sets. Let G be a finitely generated subgroup of the mapping class group Mod(S), where S is a compact orientable…

In this note we prove that every finite collection of connected algebraic subgroups of the group of triangular automorphisms of the affine space generates a connected solvable algebraic subgroup.

In this paper, we prove a series of results on group embeddings in groups with a small number of generators. We show that each finitely generated group $G$ lying in a variety ${\mathcal M}$ can be embedded in a $4$-generated group $H \in…

A finitely presented group is weakly geometrically simply connected (wgsc) if it is the fundamental group of some compact polyhedron whose universal covering is wgsc i.e. it has an exhaustion by compact connected and simply connected…

We present two uncountable families of finitely generated residually finite groups all having the same profinite completion. One consists of soluble groups, the other of branch groups.

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 introduce a class of countable groups by some abstract group-theoretic conditions. It includes linear groups with finite amenable radical and finitely generated residually finite groups with some non-vanishing $\ell^2$-Betti numbers that…

We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…

In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.

We prove the Singer conjecture for extended graph manifolds and pure complex-hyperbolic higher graph manifolds with residually finite fundamental groups. In real dimension three, where a result of Hempel ensures that the fundamental group…

We bound the size of $d$-dimensional cubulations of finitely presented groups. We apply this bound to obtain acylindrical accessibility for actions on CAT(0) cube complexes and bounds on curves on surfaces.

We define the notion of computability of F{\o}lner sets for finitely generated amenable groups. We prove, by an explicit description, that the Kharlampovich group, a finitely presented solvable group with unsolvable word problem, has…

We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.

In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.

This article gives solutions to the exercises in Bestvina and Feighn's paper on Sela's work on limit groups. We prove that all constructible limit groups are limit groups and give an account of the shortening argument of Rips and Sela.

We prove a characterization of monomial projective representations of finitely generated nilpotent groups. We also characterize polycyclic groups whose projective representations are finite dimensional.

Let $d \geq 2$ be an integer. We conjecture that there is a finitely generated perfect group whose homomorphic images include all finite $d$-generated perfect groups. We prove a special case of this conjecture for the finite perfect groups…

An l-group G is an abelian group equipped with a translation invariant lattice order. Baker and Beynon proved that G is finitely generated projective iff it is finitely presented. A unital l-group is an l-group G with a distinguished order…

It is shown that a finitely generated branch group has Serre's property (FA) if and only if it does not surject onto the infinite cyclic group or the infinite dihedral group. An example of a finitely generated self-similar branch group…

In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and…