Class-Preserving Coleman Automorphisms of Finite Groups with Prescribed Centralizers

Abstract

Let G be a finite group. It is proved that any class-preserving Coleman automorphism of G is an inner automorphism whenever G belongs to one of the following two classes of groups: (1) CN-groups, i.e., groups in which the centralizer of any element is nilpotent; (2) CIT-groups, i.e., groups of even order in which the centralizer of any involution is a 2-group. In particular, the normalizer conjecture holds for both CN-groups and CIT-groups. Additionally, some other results are also obtained.