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Some challenging group presentations

Lookup NU author(s): Professor Sarah Rees

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Abstract

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 fur 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.


Publication metadata

Author(s): Havas G, Holt DF, Kenne PE, Rees S

Publication type: Article

Publication status: Published

Journal: Journal of the Australian Mathematical Society Series A - Pure Mathematics and Statistics

Year: 1999

Volume: 67

Pages: 206-213

Print publication date: 01/10/1999

ISSN (print): 0263-6115

ISSN (electronic): 0263-6115

Publisher: Cambridge University Press

URL: http://dx.doi.org/10.1017/S1446788700001178

DOI: 10.1017/S1446788700001178


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