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- W4300837636 abstract "In this paper, we show that all Coleman automorphisms of a finite group with self-central minimal non-trivial characteristic subgroup are inner; therefore the normalizer property holds for these groups. Using our methods we show that the holomorph and wreath product of finite simple groups, among others, have no non-inner Coleman automorphisms. As a further application of our theorems, we provide partial answers to questions raised by M. Hertweck and W. Kimmerle. Furthermore, we characterize the Coleman automorphisms of extensions of a finite nilpotent group by a cyclic $p$-group. Lastly, we note that class-preserving automorphisms of 2-power order of some nilpotent-by-nilpotent groups are inner, extending a result by J. Hai and J. Ge." @default.
- W4300837636 created "2022-10-04" @default.
- W4300837636 creator A5087565364 @default.
- W4300837636 date "2017-04-20" @default.
- W4300837636 modified "2023-09-26" @default.
- W4300837636 title "Coleman automorphisms of finite groups and their minimal normal subgroups" @default.
- W4300837636 doi "https://doi.org/10.48550/arxiv.1704.06068" @default.
- W4300837636 hasPublicationYear "2017" @default.
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