English

Hydra groups

Group Theory 2015-03-13 v2

Abstract

We give examples of CAT(0), biautomatic, free-by-cyclic, one-relator groups which have finite-rank free subgroups of huge (Ackermannian) distortion. This leads to elementary examples of groups whose Dehn functions are similarly extravagant. This behaviour originates in manifestations of Hercules-versus-the-hydra battles in string-rewriting.

Keywords

Cite

@article{arxiv.1002.1945,
  title  = {Hydra groups},
  author = {Will Dison and Tim Riley},
  journal= {arXiv preprint arXiv:1002.1945},
  year   = {2015}
}

Comments

26 pages, 3 figures

R2 v1 2026-06-21T14:45:14.725Z