Related papers: Isoperimetric functions for subdirect products and…

We show that the Stallings-Bieri groups, along with certain other Bestvina-Brady groups, have quadratic Dehn function.

We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups of automatic groups which are not even…

Let $\Gamma$ be a finitely generated group and $N$ be a normal subgroup of $\Gamma$. The fiber product of $\Gamma$ with respect to $N$ is the subgroup $\Gamma \times_N \Gamma=\{(\gamma, \gamma w): \gamma \in \Gamma, w \in N\}$ of the direct…

We prove an isoperimetric inequality for groups. As an application, we obtain lower bound on F{\o}lner functions in various nilpotent-by-cyclic groups. Under a regularity assumption, we obtain a characterization of F{\o}lner functions of…

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…

We prove that if the Cayley graph of a finitely generated group enjoys the property L_delta then the group is almost convex and has a sub-cubic isoperimetric function.

We prove that there exist finitely presented, residually finite groups that are profinitely rigid in the class of all finitely presented groups but not in the class of all finitely generated groups. These groups are of the form $\Gamma…

We investigate accessible subgroups of a profinite group $G$, i.e. subgroups $H$ appearing as vertex groups in a graph of profinite groups decomposition of $G$ with finite edge groups. We prove that any accessible subgroup $H \leq G$ arises…

We show that the mapping class group of a handlebody of genus at least 2 has a Dehn function of at most exponential growth type.

In this paper it is proved that if a finitely presented group acts properly discontinuously, cocompactly and by isometries on a simply connected Riemannian manifold, then the two Dehn functions, of the group and the manifold, respectively,…

We compute the relative divergence and the subgroup distortion of Bestvina-Brady subgroups. We also show that for each integer $n\geq 3$, there is a free subgroup of rank $n$ of some right-angled Artin group whose inclusion is not a…

We determine the Dehn functions of central products of two families of filiform nilpotent Lie groups of arbitrary dimension with all simply connected nilpotent Lie groups with cyclic centre and strictly lower nilpotency class. We also…

We study conditions under which subdirect products of various types of algebraic structures are finitely generated or finitely presented. In the case of two factors, we prove general results for arbitrary congruence permutable varieties,…

We construct the first examples of finitely presented groups with quadratic Dehn function containing a finitely generated infinite torsion subgroup. These examples are "optimal" in the sense that the Dehn function of any such finitely…

We investigate the structure of subdirect products of groups, particularly their finiteness properties. We pay special attention to the subdirect products of free groups, surface groups and HNN extensions. We prove that a finitely presented…

Right-angled Artin groups and their subgroups are of great interest because of their geometric, combinatorial and algorithmic properties. It is convenient to define these groups using finite simplicial graphs. The isomorphism type of the…

We introduce the notion of $n$-split for an epimorphism from a group to a finite rank free abelian group. This is used to provide bounds for the Dehn functions of certain coabelian subgroups of direct products of finitely presented groups.…

We introduce two new types of Dehn functions of group presentations which seem more suitable (than the standard Dehn function) for infinite group presentations and prove the fundamental equivalence between the solvability of the word…

Gromov proposed an averaged version of the Dehn function and claimed that in many cases it should be subasymptotic to the Dehn function. Using results on random walks in nilpotent groups, we confirm this claim for most nilpotent groups. In…

Let $H \leq S_n$ be an intransitive group with orbits $\Omega_1, \Omega_2, \ldots ,\Omega_k$. Then certainly $H$ is a subdirect product of the direct product of its projections on each orbit, $H|_{\Omega_1} \times H|_{\Omega_2} \times…