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p-Groups with an Abelian Maximal Subgroup and Cyclic Center

Published online by Cambridge University Press:  09 April 2009

S. B. Conlon
S. B. Conlon
Affiliation:
Department of Pure Mathematics, The University of SydneySydney, N. S. W. 2006, Australia
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Abstract

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All such nonabelian finite p-groups are classified. They coincide with the class of nonabelian finite p-subgroups of GL(p, F), where F is a field, not of characteristic p, which contains all p power roots of 1, or agian with the class of all nonabelian finite subgroups of Zp= wr Zp. Various automorphism groups associated to them and their representations are calculated. Two such subgroups of GL(p, F) are conjugate as subgroups of GL(p, F) iff they are isomorphic.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 2 , September 1976 , pp. 221 - 233
Copyright
Copyright © Australian Mathematical Society 1976

References

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