On inner automorphisms of finite groups
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- by Martin R. Pettet PDF
- Proc. Amer. Math. Soc. 106 (1989), 87-90 Request permission
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
- Hermann Heineken and Hans Liebeck, The occurrence of finite groups in the automorphism group of nilpotent groups of class $2$, Arch. Math. (Basel) 25 (1974), 8–16. MR 349844, DOI 10.1007/BF01238631
- Paul E. Schupp, A characterization of inner automorphisms, Proc. Amer. Math. Soc. 101 (1987), no. 2, 226–228. MR 902532, DOI 10.1090/S0002-9939-1987-0902532-X
- U. H. M. Webb, The occurrence of groups as automorphisms of nilpotent $p$-groups, Arch. Math. (Basel) 37 (1981), no. 6, 481–498. MR 646507, DOI 10.1007/BF01234386
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 87-90
- MSC: Primary 20D45
- DOI: https://doi.org/10.1090/S0002-9939-1989-0968625-8
- MathSciNet review: 968625