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On Coxeter's families of group presentations
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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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Official URL: http://dx.doi.org/10.1016/j.jalgebra.2010.02.043
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 | ||||
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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: |
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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 |
Data sourced from Thomson Reuters' Web of Knowledge
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