Commentarii Mathematici Helvetici

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Volume 88, Issue 3, 2013, pp. 507–540
DOI: 10.4171/CMH/294

Published online: 2013-08-13

Hydra groups

Will Dison[1] and Timothy R. Riley[2]

(1) Bank of England, London, UK
(2) Cornell University, Ithaca, USA

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: Free-by-cyclic group, subgroup distortion, Dehn function, hydra

Dison Will, Riley Timothy: Hydra groups. Comment. Math. Helv. 88 (2013), 507-540. doi: 10.4171/CMH/294