Let K be a finite abelian group and let H be the holomorph of K. It is shown that every Coleman automorphism of H is an inner automorphism. As an immediate consequence of this result, it is obtained that the normalize...Let K be a finite abelian group and let H be the holomorph of K. It is shown that every Coleman automorphism of H is an inner automorphism. As an immediate consequence of this result, it is obtained that the normalizer property holds for H.展开更多
Let G be a finite group and let N be a nilpotent normal subgroup of G such that G/N is cyclic. It is shown that under some conditions all Coleman automorphisms of G are inner. Interest in such automorphisms arose from...Let G be a finite group and let N be a nilpotent normal subgroup of G such that G/N is cyclic. It is shown that under some conditions all Coleman automorphisms of G are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings.展开更多
Let G = NwrA be a wreath product of a finite nilpotent group N by an abelian group A. It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result,it is obtaine...Let G = NwrA be a wreath product of a finite nilpotent group N by an abelian group A. It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result,it is obtained that the normalizer property holds for G.展开更多
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
基金Supported by National Natural Science Foundation of China(Grant No.11171169)the Doctoral Fund of Shandong Province(Grant No.BS2012SF003)+1 种基金a Project of Shandong Province Higher Educational Science and Technology Program(Grant No.J14LI10)a Project of Shandong Province Higher Educational Excellent Backbone Teachers for International Cooperation and Training
文摘Let K be a finite abelian group and let H be the holomorph of K. It is shown that every Coleman automorphism of H is an inner automorphism. As an immediate consequence of this result, it is obtained that the normalizer property holds for H.
基金Supported by National Natural Science Foundation of China(Grant No.11171169)
文摘Let G be a finite group and let N be a nilpotent normal subgroup of G such that G/N is cyclic. It is shown that under some conditions all Coleman automorphisms of G are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171169, 11071155)Natural Science Foundation of Shandong Province (Grant No. Y2008A03)Shandong Provincial Education Department (Grant No. J07YH06)
文摘Let G = NwrA be a wreath product of a finite nilpotent group N by an abelian group A. It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result,it is obtained that the normalizer property holds for G.
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.
