Let G be a finite group with a non-central Sylow r-subgroup R, Z（G） the center of G, and N a normal subgroup of G. The purpose of this paper is to determine the structure of N under the hypotheses that N contains R ...Let G be a finite group with a non-central Sylow r-subgroup R, Z（G） the center of G, and N a normal subgroup of G. The purpose of this paper is to determine the structure of N under the hypotheses that N contains R and the G-conjugacy class size of every element of N is either i or m. Particularly, it is shown that N is Abelian if N ∩ Z（G）=1 and the G-conjugacy class size of every element of N is either 1 or m.展开更多
Let a finite group A act on a finite p-group P with ｜P｜〉 p^e, where e is an integer with e 〉 2. In this paper, we show that P is centralized by OP（A^Ap-1） if every non-maximal class p-group of order p^e in P is ...Let a finite group A act on a finite p-group P with ｜P｜〉 p^e, where e is an integer with e 〉 2. In this paper, we show that P is centralized by OP（A^Ap-1） if every non-maximal class p-group of order p^e in P is stabilized by OB（A）. As applications, someconditions are given for a finite group to be p-supersolvable.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
The Wielandt subgroup of a group G, denoted by w（G）, is the intersection of the normalizers of all subnormal subgroups of G. In this paper, the authors show that for a p-group of maximal class G, either wi（G） = ζ...The Wielandt subgroup of a group G, denoted by w（G）, is the intersection of the normalizers of all subnormal subgroups of G. In this paper, the authors show that for a p-group of maximal class G, either wi（G） = ζi（G） for all integer i or wi（G） = ζi＋1（G） for every integer i, and w（G/K） = ζ（G/K） for every normal subgroup g in G with K ≠ 1. Meanwhile, a necessary and sufficient condition for a regular p-group of maximal class satisfying w（G） = ζ2（G） is given. Finally, the authors prove that the power automorphism group PAut（G） is an elementary abelian p-group if G is a non-abelian p- group with elementary ζ（G） ∩ζ1（G）.展开更多
If H is a subgroup of a finite group G,then the automizer AutG(H)of H in G is defined as the group of automorphisms of H induced by conjugation by elements of NG(H).A finite group G is called an NNC-group if for any n...If H is a subgroup of a finite group G,then the automizer AutG(H)of H in G is defined as the group of automorphisms of H induced by conjugation by elements of NG(H).A finite group G is called an NNC-group if for any non-normal abelian subgroup A,either AutG(A)=1 or CG(A)=A.In this paper,classifications of nilpotent NNC-groups and non-solvable NNC-groups are given.We also investigate the solvable NNC-groups and describe the structure of solvable NNC-groups.展开更多
基金supported by the National Natural Science Foundation of China (22106072 and 42177356)the Fundamental Research Funds for the Central Universities (2022300301)+4 种基金the Natural Science Research Major Project of Jiangsu Higher Education Institutions of China (22KJA610003)the State Key Laboratory of Pollution Control and Resource Reuse Foundation (PCRRF21032)the Open Fund of Key Laboratory of Green Chemical Technology of Fujian Province University (WYKFGCT2022-3)China Postdoctoral Science Foundation (2022M721555)Jiangsu Funding Program for Excellent Postdoctoral Talent (2023ZB081)。
基金supported by the National Natural Science Foundation of China (No. 10771132)SGRC (No.GZ 310)the Research Grant of Shanghai University and the Shanghai Leading Academic Discipline Project (No. J50101).
文摘Let G be a finite group with a non-central Sylow r-subgroup R, Z（G） the center of G, and N a normal subgroup of G. The purpose of this paper is to determine the structure of N under the hypotheses that N contains R and the G-conjugacy class size of every element of N is either i or m. Particularly, it is shown that N is Abelian if N ∩ Z（G）=1 and the G-conjugacy class size of every element of N is either 1 or m.
基金The research was partially supported by the National Natural Science Foundation of China （11371237） and a grant of the First-Class Discipline of Universities in Shanghai.
文摘Let a finite group A act on a finite p-group P with ｜P｜〉 p^e, where e is an integer with e 〉 2. In this paper, we show that P is centralized by OP（A^Ap-1） if every non-maximal class p-group of order p^e in P is stabilized by OB（A）. As applications, someconditions are given for a finite group to be p-supersolvable.
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.
基金supported by the National Natural Science Foundation of China (No. 11071155)the Key Disciplines of Shanghai Municipality (No. S30104)
文摘The Wielandt subgroup of a group G, denoted by w（G）, is the intersection of the normalizers of all subnormal subgroups of G. In this paper, the authors show that for a p-group of maximal class G, either wi（G） = ζi（G） for all integer i or wi（G） = ζi＋1（G） for every integer i, and w（G/K） = ζ（G/K） for every normal subgroup g in G with K ≠ 1. Meanwhile, a necessary and sufficient condition for a regular p-group of maximal class satisfying w（G） = ζ2（G） is given. Finally, the authors prove that the power automorphism group PAut（G） is an elementary abelian p-group if G is a non-abelian p- group with elementary ζ（G） ∩ζ1（G）.
基金the National Natural Science Foundation of China(11771271).
文摘If H is a subgroup of a finite group G,then the automizer AutG(H)of H in G is defined as the group of automorphisms of H induced by conjugation by elements of NG(H).A finite group G is called an NNC-group if for any non-normal abelian subgroup A,either AutG(A)=1 or CG(A)=A.In this paper,classifications of nilpotent NNC-groups and non-solvable NNC-groups are given.We also investigate the solvable NNC-groups and describe the structure of solvable NNC-groups.
