Submission date: 18 December 2020

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 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.

Mathematics Subject Classification: 20F05, 20F06, 20F65, 03D10

Keywords and phrases:

Full text arXiv 2012.10417: pdf, ps.