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A computer proof of relations in a certain class of groups

Published online by Cambridge University Press:  14 November 2011

Edmund F. Robertson
Affiliation:
Department of Mathematical Sciences, University of St Andrews, Mathematical Institute, North Haugh, St Andrews KY16 9SS, Scotland, U.K
Kevin Rutherford
Affiliation:
Department of Mathematical Sciences, University of St Andrews, Mathematical Institute, North Haugh, St Andrews KY16 9SS, Scotland, U.K

Synopsis

A gp-toolkit consisting of computer implementations of various group theory methods, in particular a Tietze transformation program, was designed. Special cases of a conjecture were solved by the gp-toolkit. Examination of the method used by the gp-toolkit to deduce relations showed that a general approach had been employed. We present a proof verifying that the conjecture is true which is a straightforward generalisation of the method discovered by the gp-toolkit.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1991

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References

1Campbell, C. M. and Robertson, E. F.. Deficiency zero groups involving Fibonacci and Lucas numbers. Proc. Roy. Soc. Edinburgh Sect. A 81 (1978), 273286.CrossRefGoogle Scholar
2Campbell, C. M. and Robertson, E. F.. Some problems in group presentations. J. Korean Math. Soc. 19 (1983), 5964.Google Scholar
3Havas, G., Kenne, P. E., Richardson, J. S. and Robertson, E. F.. A Tietze transformation program. In Computational Group Theory, pp. 6974 (London: Academic Press, 1984).Google Scholar
4Rutherford, K.. Computational techniques applied to group presentations (Ph.D. Thesis, University of St Andrews, 1989).Google Scholar

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