Algorithmic problems in groups with quadratic Dehn function

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2020-12-18 DOI:10.4171/ggd/694

A. Olshanskii, M. Sapir

引用次数: 3

Abstract

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 QDgroups. (2) For every recursive function f , there is a QD-group G containing a finitely presented subgroup H whose Dehn function grows faster than f . (3) There exists a group with undecidable conjugacy problem but decidable power conjugacy problem; this group is QD.

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二次Dehn函数群的算法问题

我们构造和研究了具有二次Dehn函数的有限呈现群（QD群），并介绍了我们最近论文中开发的方法的以下应用。（1）同构问题在量子群类中是不可判定的。（2）对于每个递归函数f，都有一个QD群G，它包含一个有限存在的子群H，其Dehn函数的增长速度快于f。（3）存在一个具有不可判定共轭问题但具有可判定幂共轭问题的群；这个组是QD。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.