Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem

Torsion Subgroups of Groups with Cubic Dehn Function

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 can be embedded as a subgroup of a finitely presented group with cubic Dehn function.

Torsion Subgroups of Groups with Quadratic Dehn Function

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 presented group must be at least quadratic. Moreover, we show that for any $n\geq2^{48}$ such that $n$ is either odd or divisible by $2^9$, any infinite free Burnside group with exponent $n$ is a quasi-isometrically embedded subgroup of a finitely presented group with quadratic Dehn function satisfying the Congruence Extension Property.

On Dehn functions of infinite presentations of 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 problem for a group presentation defined by a decidable set of defining words and the property of being computable for one of the newly introduced functions (this equivalence fails for the standard Dehn function). Elaborating on this equivalence and making use of this function, we obtain a characterization of finitely generated groups for which the word problem ca…

有限生成群中的等周不等式

Isoperimetric inequalities in finitely generated groups

本文研究了有限生成群的Dehn谱，计算了多种群的Dehn谱，并证明了存在不可数多个非准等距的有限生成群。

拟等距 Higman 嵌入与 Dehn 函数

Quasi-isometric Higman embeddings and the Dehn function

本文证明满足特定计算枚举条件的有限生成群可拟等距嵌入到 Dehn 函数受计算复杂度控制的有限呈现群中，推广了自由 Burnside 群嵌入结果，并改进了字问题 NP 性与多项式 Dehn 函数嵌入的经典刻画。

Twisted conjugacy separable groups

We study the notion of twisted conjugacy separability (essentially introduced in our previous paper for a proof of twisted version of Burnside-Frobenius theorem) and some related properties. We give examples of groups with and without this property and study its behavior under some extensions. An affirmative answer to the twisted Dehn conjugacy problem for polycyclic-by-finite group is obtained. Some problems for the further study are indicated.