Related papers: Torsion Subgroups of Groups with Quadratic Dehn Fu…
We construct the first examples of finitely presented groups with cubic Dehn function containing a finitely generated infinite torsion subgroup. Moreover, we show that any infinite free Burnside group with sufficiently large odd exponent…
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…
Baumslag's group is a finitely presented metabelian group with a Z \wr Z subgroup. There is an analogue with an additional torsion relation in which this subgroup becomes C_m \wr Z. We prove that Baumslag's group has an exponential Dehn…
We construct a finitely presented group with undecidable word problem and with Dehn function bounded by a quadratic function on an infinite set of positive integers.
We construct examples of finitely presented simple groups whose Dehn functions are at least exponential. To the best of our knowledge, these are the first such examples known. Our examples arise from R\"over-Nekrashevych groups, using…
We prove that the Bridson-Dison group has quartic Dehn function, thereby providing the first precise computation of the Dehn function of a subgroup of a direct product of free groups with super-quadratic Dehn function. We also prove that…
We construct easy embeddings of relatively free groups (say the free Burnside group, the free solvable group) into finitely presented groups. We introduce a concept of verbal isoperimetric function of a group variety. We prove that if the…
We construct an embedding of a free Burnside group $B(m,n)$ of odd $n > 2^{48}$ and rank $m >1$ in a finitely presented group with some special properties. The main application of this embedding is an easy construction of finitely presented…
It is shown that there exist infinitely many non-integers $r>2$ such that the Dehn function of some finitely presented group is $\simeq n^r$. For each positive rational number $s$ we construct pairs of finitely presented groups $H\subset G$…
Subgroups of direct products of finitely many finitely generated free groups form a natural class that plays an important role in geometric group theory. Its members include fundamental examples, such as the Stallings-Bieri groups. This…
This is the first of a sequence of papers devoted to studying the link between the complexity of the Word Problem for a finitely generated recursively presented group $G$ and the isoperimetric functions of the finitely presented groups in…
To each finitely generated group $G$, we associate a quasi-isometric invariant called the \emph{Dehn spectrum} of $G$. If $G$ is finitely presented, our invariant is closely related to the Dehn function of $G$, but provides more information…
We show the connection between the relative Dehn function of a finitely generated metabelian group and the distortion function of a corresponding subgroup in the wreath product of two free abelian groups of finite rank. Further, we show…
On the one hand, it is well known that the only subquadratic Dehn function of finitely presented groups is the linear one. On the other hand there is a huge class of Dehn functions $d(n)$ with growth at least $n^4$ (essentially all possible…
We establish a cubic lower bound on the Dehn function of a certain finitely presented subgroup of a direct product of 3 free groups.
In this paper, we compute an upper bound for the Dehn function of a finitely presented metabelian group. In addition, we prove that the same upper bound works for the relative Dehn function of a finitely generated metabelian group. We also…
We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a…
We construct and study finitely presented groups with quadratic Dehn function (QD-groups) and present the following applications of the method developed in our recent papers. (1) The isomorphism problem is undecidable in the class of…
Given a finitely presented group $G$ and a surjective homomorphism $G\to \mathbb{Z}^n$ with finitely presented kernel $K$, we give an upper bound on the Dehn function of $K$ in terms of an area-radius pair for $G$. As a consequence we…
We address the problem of which functions can arise as Dehn functions of K\"ahler groups. We explain why there are examples of K\"ahler groups with linear, quadratic, and exponential Dehn function. We then proceed to show that there is an…