Some challenging group presentations

George Havas, Derek F. Holt, P.E.Kenne, and Sarah Rees


group presentations, Knuth-Bendix, Todd-Coxeter


In J. Austral. Math. Soc. 67 (1999) 137-163


We study some challenging presentations which arise as groups of deficiency zero. In four cases we settle finiteness: we show that two presentations are for finite groups while two are for infinite groups. Thus we answer three explicit questions in the literature and we provide the first published deficiency zero presentation for a group with derived length seven. The tools we use are coset enumeration and Knuth-Bendix rewriting, which are well-established as methods for proving finiteness or otherwise of a finitely presented group. We briefly comment on their capabilities and compare their performance. \

The preprint is available as gzipped dvi (14 kB) and postscript (63 kB) files.

Alternatively, you can request a copy by e-mailing me.

Sarah Rees
05 May 1999