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 ...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.展开更多
基金The research of the work was partially supported by the National Natural Science Foundation of China(11771271).
文摘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.
