Related papers: An elementary proof that subgroups of free groups …

We give a complete classification of finitely generated virtually free groups up to $\forall\exists$-elementary equivalence. As a corollary, we give an algorithm that takes as input two finite presentations of virtually free groups, and…

Recall that a pseudofree group action on a space is one whose singular set consists only of isolated points. In this paper, we classify all of the finite groups which admit pseudofree actions on S^2 x S^2. The groups turn out to be exactly…

We prove that the outer automorphism group of a free group of countably infinite rank is complete.

A well known theorem of Burns and Romanovskii states that a free product of subgroup separable groups is itself subgroup separable. We provide a proof using the language of immersions and coverings of graphs of groups, due to Bass.

We prove that every simplicial automorphism of the free splitting graph of a free group of at least rank 3 is induced by an outer automorphism of the free group.

We construct an uncountable sequence of groups acting uniformly properly on hyperbolic spaces. We show that only countably many of these groups can be virtually torsion-free. This gives new examples of groups acting uniformly properly on…

Answering a question due to Min, we prove that a finite graph of roses admits a regluing such that the resulting graph of roses has hyperbolic fundamental group.

This paper describes a simple method for estimating lower bounds on the number of classes of equivalence for a special kind of integer sequences, called division sequences. The method is based on adding group structure to classes of…

We deduce direct formulas for the total number of subgroups and the number of subgroups of a given order of the group $\Bbb{Z}_m\times \Bbb{Z}_n \times \Bbb{Z}_r \times \Bbb{Z}_s$, where $m,n,r,s\in \Bbb{N}$. The proofs are by some simple…

We introduce notions of absolutely non-free and perfectly non-free group actions and use them to study the associated unitary representations. We show that every weakly branch group acts absolutely non-freely on the boundary of the…

In this work, we prove that if a triangular algebra $A$ admits a strongly simply connected universal Galois covering for a given presentation then the fundamental group associated to this presentation is free.

We develop a method to show that some (abstract) groups can be embedded into a free pro-$p$ group. In particular, we show that a finitely generated subgroup of a free $\mathbb Q$-group can be embedded into a free pro-$p$ group for almost…

We classify the finite groups $G$ such that the group of units of the integral group ring ${\mathbb Z} G$ has a subgroup of finite index which is a direct product of free-by-free groups.

In this paper, we introduce the notion of $L^2$-subgroup rigid groups and demonstrate that free groups are $L^2$-subgroup rigid. As a consequence, we establish the equivalence between compressibility, inertness, strong inertness, and…

We introduce a family of atomic measures on free groups generated by no-return random walks. These measures are shown to be very convenient for comparing "relative sizes" of subgroups, context-free and regular subsets (that, subsets…

Let G be an acylindrically hyperbolic group. We consider a random subgroup H in G, generated by a finite collection of independent random walks. We show that, with asymptotic probability one, such a random subgroup H of G is a free group,…

Let G be a finitely generated free, free abelian of arbitrary exponent, free nilpotent, or free solvable group, or a free group in the variety A_mA_n, and let A = {a_1,..., a_r} be a basis for G. We prove that, in most cases, if S is a…

Consider a relatively hyperbolic group G. We prove that if G is finitely presented, so are its parabolic subgroups. Moreover, a presentation of the parabolic subgroups can be found algorithmically from a presentation of G, a solution of its…

The known facts about solvability of equations over groups are considered from a more general point of view. A generalized version of the theorem about solvability of unimodular equations over torsion-free groups is proved. In a special…

A subgroup $H$ of a free group $F$ is called inert in $F$ if for every $G < F$ the rank of the intersection of $H$ with $G$ is no grater than the rank of $G$. In this paper we expand the known families of inert subgroups. We show that the…