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Lookup NU author(s): Professor Sarah Rees
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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.
Author(s): Havas G, Holt DF, Kenne PE, Rees S
Publication type: Article
Publication status: Published
Journal: Journal of the Australian Mathematics Society
Year: 1999
Volume: 67
Issue: 2
Pages: 206-213
Print publication date: 01/10/1999
ISSN (print): 1446-7887
ISSN (electronic): 1446-8107
Publisher: Cambridge University Press
URL: http://dx.doi.org/10.1017/S1446788700001178
DOI: 10.1017/S1446788700001178
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