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An algorithm for determining defining relations of a subgroup

Published online by Cambridge University Press:  18 May 2009

D. H. McLain
D. H. McLain
Affiliation:
Computing Centre, University of Sheffield, Sheffield
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Suppose that G is a finitely presented group, and that we are given a set of generators for a subgroup H of finite index in G. In this paper we describe an algorithm by which a set of defining relations may be found for H in these generators.

The algorithm is suitable for programming on a digital computer. It appears to have significant computational advantages over the method of Mendelsohn [8] (which is based on the Schreier-Reidemeister results, see for example [4, pp. 91–95]) in those cases where the generators of H are given as other than the familiar Schreier-Reidemeister generators.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 1 , January 1977 , pp. 51 - 56
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

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