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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On inner automorphisms of finite groups


Author: Martin R. Pettet
Journal: Proc. Amer. Math. Soc. 106 (1989), 87-90
MSC: Primary 20D45
MathSciNet review: 968625
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Abstract: It is shown that in certain classes of finite groups, inner automorphisms are characterized by an extension property and also by a dual lifting property. This is a consequence of the fact that for any finite group $ G$ and any prime $ p$, there is a $ p$-group $ P$ and a semidirect product $ H = GP$ such that $ P$ is characteristic in $ H$ and every automorphism of $ H$ induces an inner automorphism on $ H/P$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0968625-8
PII: S 0002-9939(1989)0968625-8
Article copyright: © Copyright 1989 American Mathematical Society