Some challenging group presentations
George Havas, Derek F. Holt, P.E.Kenne,
and Sarah Rees
Keywords group presentations, Knuth-Bendix, Todd-Coxeter
Status 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.
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05 May 1999.