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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$.

References [Enhancements On Off] (What's this?)

  • [1] H. Heineken and H. Liebeck, The occurrence of finite groups in the automorphism group of nilpotent groups of class 2, Arch. Math. 25 (1974), 8-16. MR 0349844 (50:2337)
  • [2] P. E. Schupp, A characterization of inner automorphisms, Proc. Amer. Math. Soc. 101 (1987), 226-228. MR 902532 (89b:20070)
  • [3] U. H. M. Webb, The occurrence of groups as automorphisms of nilpotent $ p$-groups, Arch. Math. 37 (1981), 481-498. MR 646507 (84g:20071)

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Article copyright: © Copyright 1989 American Mathematical Society

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