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A class of two generator two relation finite groups

Published online by Cambridge University Press:  09 April 2009

J. W. Wamsley
J. W. Wamsley
Affiliation:
School of Mathematical Sciences The Flinders University of South AustraliaBeford Park, South Australia, 5042, Australia
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A group which is minimally generated by n generators and defined by n relations is said to have zero deficiency. The class of finite groups known to have zero deficiency is small, consisting of cyclic groups, certain metacyclic groups [4] and classes of groups given in [1], [2] and [3].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 1 , July 1972 , pp. 38 - 40
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]MacDonald, I. D., ‘On a class of finitely presented groups’, Canad. J. Math. 14 (1962), 602–613.CrossRefGoogle Scholar
[2]Mennicke, J., ‘Einige endlicke Gruppen mit drei Erzeugenden und drei Relationen’, Archiv der Math. 10 (1959), 409–418.CrossRefGoogle Scholar
[3]Wamsley, J. W., ‘A class of three generator three relation finite groups’, Canad. J. Math. 22 (1970), 36–40.CrossRefGoogle Scholar
[4]Wamsley, J. W., ‘The deficiency of metacyclc groups’, Proc. Amer. Math. Soc. 24 (1970), 724–726.Google Scholar