Some challenging group presentations
Published online by Cambridge University Press: 09 April 2009
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-Bebdix 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.
- Research Article
- Journal of the Australian Mathematical Society , Volume 67 , Issue 2 , October 1999 , pp. 206 - 213
- Copyright © Australian Mathematical Society 1999
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