Algorithmic problems in groups with quadratic Dehn function

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 QD-groups. (2) For every recursive function f , there is a QD-grou...

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Published in:Groups, geometry and dynamics geometry and dynamics, 2022-01, Vol.16 (4), p.1289-1339
Main Authors: Olshanskii, Alexander Yu, Sapir, Mark V.
Format: Article
Language:English
Online Access:Get full text
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Summary: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 QD-groups. (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.
ISSN:1661-7207
1661-7215
DOI:10.4171/ggd/694