English

Algorithmic problems in groups with quadratic Dehn function

Group Theory 2020-12-21 v1

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 ff, there is a QD-group GG containing a finitely presented subgroup HH whose Dehn function grows faster than ff. (3) There exists a group with undecidable conjugacy problem but decidable power conjugacy problem; this group is QD.

Keywords

Cite

@article{arxiv.2012.10417,
  title  = {Algorithmic problems in groups with quadratic Dehn function},
  author = {A. Yu. Olshanskii and M. V. Sapir},
  journal= {arXiv preprint arXiv:2012.10417},
  year   = {2020}
}

Comments

45 pages. arXiv admin note: text overlap with arXiv:1809.00280