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coleman automorphisms of Holomorphs of Finite Abelian Groups

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Acta Mathematica Sinica,English Series 2014年第9期30卷 1549-1554页

作者： Zheng Xing LI Jin Ke HAI College of Mathematics Qingdao University

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... 详细信息

关键词： coleman automorphism integral group ring the normalizer property

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coleman automorphisms of Generalized Dihedral Groups

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Acta Mathematica Sinica,English Series 2016年第2期32卷 251-257页

作者： Zheng Xing LI Yuan Lin LI Colledge of Automation EngineeringQingdao University Department of Mathematics Brock University

Let D be a generalized dihedral group and Autcol（D） its coleman automorphism group. Denote by Outcol（D） the quotient group of Autcol（D） by Inn（D）, where Inn（D） is the inner automorphism group of D. It is proved that either Outcol（D） = i or Outcol（D） is an elementary abelian 2-group whose order is completely determined by the cardinality of π（D）. Furthermore, a necessary and sufficient condition for Outcol（D） = 1 is obtained. In addition, whenever Outcol（D） ≠ 1, it is proved that Autcol（D） is a split extension of Inn（D） by an elementary abelian 2-group for which an explicit description is given.

关键词： coleman automorphism generalized dihedral group

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coleman automorphisms of Finite Groups with a Unique Nontrivial Normal Subgroup

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Journal of Mathematical Research with Applications 2014年第3期34卷 301-306页

作者： Zhengxing LI Jinke HAI Shuxian YANG College of Mathematics Qingdao University

Let G be a finite group with a unique nontrivial normal subgroup. It is shown that every coleman automorphism of G is an inner automorphism.

关键词： coleman automorphism minimal normal subgroup.

On coleman automorphisms of Finite Nilpotent Groups by Cyclic Groups

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Acta Mathematica Sinica,English Series 2016年第12期32卷 1459-1464页

作者： Jin Ke HAI Sheng Bo GE College of Mathematics and Statistics Qingdao University

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... 详细信息

关键词： coleman automorphism the normalizer property nilpotent group

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Class-Preserving coleman automorphisms of Finite Groups with Prescribed Centralizers

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Algebra Colloquium 2017年第2期24卷 351-360页

作者： Zhengxing Li Hongwei Gao College of Automation and Electrical Engineering Qingdao University Qingdao Shandong 266071 China School of Mathematics and Statistics Qingdao University Qingdao Shandong 266071 China Institute of Applied Mathematics of Shandong Qingdao Shandong 266071 China

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.

关键词： class-preserving automorphism coleman automorphism integral group ring,the normalizer conjecture

Class-Preserving coleman automorphisms of Finite Groups Whose Second Maximal Subgroups Are TI-Subgroups

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Journal of Mathematical Research with Applications 2013年第2期33卷 241-245页

作者： Zhengxing LI Jinke HAI College of Mathematics Qingdao University

Recall that a subgroup H of a finite group G is called a TI-subgroup if H ∩ Hg= 1 or H for each g ∈ *** that G is a finite group whose second maximal subgroups are *** is shown that every class-preserving coleman automorphism of G is an inner *** an immediate consequence of this result,we obtain that the normalizer property holds for G.

关键词： normalizer property coleman automorphism class-preserving automorphism.

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

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Communications in Mathematics and Statistics 2021年第1期9卷 87-99页

作者： Tao Zheng Xiuyun Guo Department of Mathematics Shanghai UniversityShanghai 200444People’s Republic of China

In this paper we mainly investigate the coleman automorphisms and class-preserving automorphisms of finite AZ-groups and finite groups related to *** example,we first prove that Outc(G)of an AZ-group G must be a 2′-group and therefore the normalizer property holds for *** 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 ***,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

On p-Central automorphisms of Primitive Groups and Applications

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Journal of Mathematical Research with Applications 2019年第1期39卷 23-30页

作者： Shenjuan DONG Zhengxing LI School of Mathematics and Statistics Qingdao University Institute of Applied Mathematics of Shandong

Let G be a primitive group. It is proved that there exits some prime p such that every p-central automorphism of G is inner. As an application, it is proved that every coleman automorphism of the holomorph of G is inner. In particular, the normalizer property holds for such groups in question. Additionally, other related results are obtained as well.

关键词： p-central automorphism coleman automorphism the normalizer conjecture