On class-preserving Coleman automorphisms of semidirect products of finite nilpotent groups by finite groups. (English) Zbl 1399.20038

Hai, J.; Ge, S.

Publ. Math. 90, No. 1-2, 217-226 (2017).

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

Keywords:

semidirect product; class-preserving automorphism; Coleman automorphism; normalizer property