English

Hydra group doubles are not residually finite

Group Theory 2015-07-31 v2

Abstract

In 2013, Kharlampovich, Myasnikov, and Sapir constructed the first examples of finitely presented residually finite groups with large Dehn functions. Given any recursive function ff, they produce a finitely presented residually finite group with Dehn function dominating ff. There are no known elementary examples of finitely presented residually finite groups with super-exponential Dehn function. Dison and Riley's hydra groups can be used to construct a sequence of groups for which the Dehn function of the k-th group is equivalent to the k-th Ackermann function. Kharlampovich, Myasnikov, and Sapir asked whether or not these groups are residually finite. We show that these constructions do not produce residually finite groups.

Cite

@article{arxiv.1507.02554,
  title  = {Hydra group doubles are not residually finite},
  author = {Kristen Pueschel},
  journal= {arXiv preprint arXiv:1507.02554},
  year   = {2015}
}

Comments

8 pages - updated Lemma 2.1 and removed typos

R2 v1 2026-06-22T10:08:50.978Z