Related papers: The generalised word problem for subgroups of hype…

This paper describes some generalizations of the results presented in the book "Geometry of defining Relations in Groups" , of A.Yu.Ol'shanskii to the case of non-cyclic torsion-free hyperbolic groups. In particular, it is proved that for…

Suppose that a finitely generated group $G$ is hyperbolic relative to a collection of subgroups $\mathbb{P}=\{P_1,\dots,P_m\}$. Let $H_1,H_2$ be subgroups of $G$ such that $H_1$ is relatively quasiconvex with respect to $\mathbb{P}$ and…

The co-word problem of a group G generated by a set X is defined as the set of words in X which do not represent 1 in G. We introduce a new method to decide if a permutation group has context-free co-word problem. We use this method to…

We describe an algorithm for deciding whether or not a given finitely generated torsion-free nilpotent group is decomposable as the direct product of nontrivial subgroups.

We show that, given a finitely generated group $G$ as the coordinate group of a finite system of equations over a torsion-free hyperbolic group $\Gamma$, there is an algorithm which constructs a cover of a canonical solution diagram. The…

We refine Feighn--Handel's results on subgroups of mapping tori of free groups to the special case of free-by-cyclic groups. We use these refinements to show that any finitely generated free-by-cyclic group embeds in a {finitely generated…

This paper addresses the torsion problem for a class of automaton semigroups, defined as semigroups of transformations induced by Mealy automata, aka letter-by-letter transducers with the same input and output alphabet. The torsion problem…

We call a finitely generated group lacunary hyperbolic if one of its asymptotic cones is an R-tree. We characterize lacunary hyperbolic groups as direct limits of Gromov hyperbolic groups satisfying certain restrictions on the hyperbolicity…

Suppose $G$ is a 1-ended finitely generated group that is hyperbolic relative to P a finite collection of 1-ended finitely generated subgroups. Our main theorem states that if the boundary $\partial (G, P)$ has no cut point, then $G$ has…

In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domains in real projective space. We also establish a…

In this paper, we study the word problem for automaton semigroups and automaton groups from a complexity point of view. As an intermediate concept between automaton semigroups and automaton groups, we introduce automaton-inverse semigroups,…

The Equation Problem in finitely presented groups asks if there exists an algorithm which determines in finite amount of time whether any given equation system has a solution or not. We show that the Equation Problem in central extensions…

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…

We consider the class $\mathcal{R}$ of finitely generated toral relatively hyperbolic groups. We show that groups from $\mathcal{R}$ are commutative transitive and generalize a theorem proved by Benjamin Baumslag to this class. We also…

This note proves a generalisation to inverse semigroups of Anisimov's theorem that a group has regular word problem if and only if it is finite, answering a question of Stuart Margolis. The notion of word problem used is the two-tape word…

We prove that, if a group is relatively hyperbolic, the parabolic subgroups are virtually nilpotent if and only if there exists a hyperbolic space with bounded geometry on which it acts geometrically finitely. This provides, by use of M.…

As a common non-trivial generalization of the notion of a generalized co-Bassian group, recently defined by the third author, we introduce the notion of a semi-generalized co-Bassian group and initiate its comprehensive study. Specifically,…

Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable;…

We prove that the word problem of the Brin-Thompson group nV over a finite generating set is coNP-complete for every n \ge 2. It is known that the groups nV are an infinite family of infinite, finitely presented, simple groups. We also…

In 2006 Z. Sela and independently O. Kharlampovich and A. Myasnikov gave a solution to the Tarski problems by showing that two non-abelian free groups have the same elementary theory. Subsequently Z. Sela generalized the techniques used in…