Class-Preserving Coleman Automorphisms of Finite Groups with Prescribed Centralizers

• 来源期刊: 代数集刊（英文版）
• 关键词: class-preserving automorphism Coleman automorphism integral group ring the normalizer conjecture
• 年，卷（期）: 2017,（2）
• 页码范围: 351-360
• 页数: 10页
• 语种: 英文
• DOI: 10.1142/S1005386717000219

摘要

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.