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 wh...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.展开更多
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Supported by the National Natural Science Foundation of China （71571108）, Projects of International （Regional） Cooperation and Exchanges of NSFC （71611530712, 61661136002）, Specialized Research Fund for the Doctoral Program of Higher Education of China （20133706110002）, Natural Science Foundation of Shandong Province （ZR2015GZ007） Project Funded by China Postdoctoral Science Foundation （2016M590613）, Specialized Fund for the Postdoctoral Innovative Research Program of Shandong Province （201602035）, Project of Shandong Province Higher Educational Science and Technology Program （J14LI10） and Project of Shandong Province Higher Edu- cational Excellent Backbone Teachers for International Cooperation and Training.
文摘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.
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.
