UNSPECIFIED (1999) Some challenging group presentations. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 67 (Part 2). pp. 206-213. ISSN 0263-6115

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
Publisher:	AUSTRALIAN MATHEMATICS PUBL ASSOC INC
ISSN:	0263-6115
Date:	October 1999
Volume:	67
Number:	Part 2
Number of Pages:	8
Page Range:	pp. 206-213
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/14050

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