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Proving a group trivial made easy: A case study in coset enumeration

Published online by Cambridge University Press:  17 April 2009

George Havas  and
Colin Ramsay
George Havas
Affiliation:
Centre for Discrete Mathematics and Computing, Department of Computer Science and Electrical Engineering, The University of Queensland, Queensland 4072Australia, e-mail: havas@csee.uq.edu.aucram@csee.uq.edu.au
Colin Ramsay
Affiliation:
Centre for Discrete Mathematics and Computing, Department of Computer Science and Electrical Engineering, The University of Queensland, Queensland 4072Australia, e-mail: havas@csee.uq.edu.aucram@csee.uq.edu.au
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Abstract

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Coset enumeration, based on the methods described by Todd and Coxeter, is one of the basic tools for investigating finitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. Here we consider one such family of presentations proposed by B.H. Neumann. We show that the problems are much easier than they first appear, albeit at the expense of considerable preliminary ‘experimentation’. This demonstrates how far the range of applicability of coset enumeration has improved.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 1 , August 2000 , pp. 105 - 118
Copyright
Copyright © Australian Mathematical Society 2000

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