The Normalizer Property for Finite GroupsWhose Sylow 2-Subgroups are Abelian  

作　　者：Tao Zheng Xiuyun Guo 

机构地区：[1]Department of Mathematics,Shanghai University,Shanghai 200444,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2021年第1期87-99,共13页数学与统计通讯（英文）

基　　金：The research of the work was partially supported by the National Natural Science Foundation of China(11771271).

摘　　要：In this paper we mainly investigate the Coleman automorphisms and class-preserving automorphisms of finite AZ-groups and finite groups related to AZ-groups.For example,we first prove that Outc(G)of an AZ-group G must be a 2′-group and therefore the normalizer property holds for G.Then we find some classes of finite groups such that the intersection of their outer class-preserving automorphism groups and outer Coleman automorphism groups is 2′-groups,and therefore,the normalizer property holds for these kinds of finite groups.Finally,we show that the normalizer property holds for the wreath products of AZ-groups by rational permutation groups under some conditions.

关 键 词：Class-preserving automorphism Coleman automorphism Normalizer property AZ-group 

分 类 号：O15[理学—数学]