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power automorphism

Proceedings of the Edinburgh Mathematical Society (1)

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THE EMBEDDING OF A CYCLIC PERMUTABLE SUBGROUP IN A FINITE GROUP. II
J. Cossey, S. E. Stonehewer
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 47 / Issue 1 / February 2004

Published online by Cambridge University Press:

27 May 2004, pp. 101-109
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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