Havas, George and Holt, Derek F. (2010) On Coxeter's families of group presentations. Journal of Algebra, Vol.324 (No.5). pp. 1076-1082. doi:10.1016/j.jalgebra.2010.02.043 ISSN 0021-8693.

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Abstract

In 1939 Coxeter published three infinite families of group presentations. He studied their properties, in particular determining when groups defined by members of the families are infinite and the structure of finite ones. Eight presentations remained for which the finiteness question was unsettled. We show that two of these eight presentations define finite groups (for which we give comprehensive proofs and provide detailed structural information) and that two of the presentations define infinite groups. Our results rely on substantial amounts of computer calculations, in particular on coset enumeration to prove finiteness and on computation of automatic structures using Knuth-Bendix rewriting to prove infiniteness. (C) 2010 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Journal of Algebra
Publisher:	Academic Press Inc Elsevier Science
ISSN:	0021-8693
Official Date:	1 September 2010
Dates:	Date Event 1 September 2010 Published
Volume:	Vol.324
Number:	No.5
Number of Pages:	7
Page Range:	pp. 1076-1082
DOI:	10.1016/j.jalgebra.2010.02.043
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Australian Research Council

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