Some challenging group presentations
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 0263-6115Full text not available from this repository.
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|
|Number of Pages:||8|
|Page Range:||pp. 206-213|
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