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On p-groups with a cyclic commutator subgroup

Published online by Cambridge University Press:  09 April 2009

R. J. Miech
R. J. Miech
Affiliation:
Department of Mathematics University of CaliforniaLos Angeles, 90024, U. S. A.
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This paper contains the complete classification of the finite p-groups G where p is an odd prime, G is generated by two elements, and the commutator subgroup of G is cyclic. These groups are a special kind of two-generator metabelian group, a class that has been studied by Szekeres (1965). He determined the defining relations of such groups but, as he noted, a “residual isomorphism problem” remains. The cyclic commutator groups are simple when considered from this first point of view; they have a short, easily derived set of defining relations. However, the isomorphism problem is a bit complicated for the defining relations contain nine parameters and each of these parameters might and can be an invariant of the group.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 2 , September 1975 , pp. 178 - 198
Copyright
Copyright © Australian Mathematical Society 1975

References

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