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THE EMBEDDING OF A CYCLIC PERMUTABLE SUBGROUP IN A FINITE GROUP. II

Published online by Cambridge University Press:  27 May 2004

J. Cossey  and
S. E. Stonehewer
J. Cossey
Affiliation:
Department of Mathematics, Australian National University, Canberra, ACT 0200, Australia ([email protected])
S. E. Stonehewer
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK ([email protected])
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Abstract

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In two previous papers we established the structure of the normal closure of a cyclic permutable subgroup $A$ of a finite group, first when $A$ has odd order and second when $A$ has even order, but with an extra hypothesis that was unnecessary in the odd case. Here we describe the most general situation without any restrictions on $A$.

AMS 2000 Mathematics subject classification: Primary 20D35; 20D40

Keywords

cyclic subgrouppermutable subgrouppower automorphism
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 1 , February 2004 , pp. 101 - 109
Copyright
Copyright © Edinburgh Mathematical Society 2004