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On class-preserving Coleman automorphisms of semidirect products of finite nilpotent groups by finite groups. (English) Zbl 1399.20038
Summary: Let \(G\) be a semidirect product of a finite nilpotent group by a finite group. It is shown that under some conditions class-preserving Coleman automorphisms of 2-power order of \(G\) are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings.

MSC:
20D45 Automorphisms of abstract finite groups
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
20D40 Products of subgroups of abstract finite groups
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