在其Sylow子群上作用双传递的有限群

本文完全确定了下述类型的有限群：（１）对于某个素数ｐ，在其Ｓｙｌｏｗｐ－子群的集合上作用双传递的所有几乎单群；（２）所有的非交换单群Ｔ，其自同构群在Ｔ的某个Ｓｙｌｏｗｐ－子群的集合上作用双传递；（３）在其所有的Ｓｙｌｏｗ子群上双传递的全部有限群．     

Frattini子群循环的有限$p$-群中的非交换集和极大Abel子群

设G是一个群,X是G的一个子集,若对于任意x,y∈X且x≠y,都有xy≠yx,则称X是G的一个非交换集.进一步,如果对于G中的任意其它非交换子集Y,都有|X|≥|Y|,那么称X是G的一个极大非交换集.文中确定了Frattini子群循环的有限p-群中极大非交换集和极大Abel子群的势.     

具有循环极大子群的亚循环p-群的自同构群

利用半直积和群扩张的理论,给出了具有极大循环子群的亚循环p-群的自同构群.     

有限群的Coleman外自同构群是p''-群的一些充分条件

本文研究了有限群G的Coleman外自同构群是p'-群这个问题. 利用Sylow p-子群和同调群的性质,得到了有限群的Coleman外自同构群是p'-群的一些充分条件,其结果与M.Hertweck和W.Kimmerle得到的结果是不同的.     

一类中心循环的有限p-群的自同构群的研究

本文研究了一类中心循环的有限p-群G的自同构群.利用在G的导群上作用平凡的自同构以及环上的辛群和正交群,确定了G的自同构群的结构,这推广了Bornand的相应结果.     

有限群的Coleman外自同构群是p＇-群的一些充分条件

本文研究了有限群G的Coleman外自同构群是p＇-群这个问题.利用Sylowp-子群和同调群的性质,得到了有限群的Coleman外自同构群是p＇-群的一些充分条件,其结果与M.Hertweck和W.Kimmerle得到的结果是不同的.     

有限交涣p群的自同构群的阶的几点注记

本文用有限交换 P 群的自同构的阶的公式,讨论了有限交换 P 群及其自同构群的阶的关系,并证明各型 P~n 阶交换群适当排列以后,其自同构群的阶依次整除。由此推广了[2]、[3]中的相应结果。以下均设 G 是 P~n 阶交换群。G 的型为     

中心循环的有限p-群中的非交换集

设G是一个群,X是G的一个子集,若对于任意x,y∈X且x≠y,都有xy≠yx,则称X是G的一个非交换集.进一步,如果对于G中的任意其他非交换子集Y,都有|X|≥|Y|,那么称X是G的一个极大非交换集.本文界定了中心循环的有限p-群中极大非交换集的势.     

交换自同构群的一个重要结论

给出一些新的方法,证明两类交换群不能作为有限群的自同构群,使MacHale提出的问题得到了突破性的进展,所给的方法具有普遍性。     

充当自同构群的有限群的几点注记

设p为奇素数,本文给出了中心循环中心商的阶小于p^5的有限p-群的完全分类并且给出它们中无对合自同构的群的自同构群的阶。由此,我们找到了能作为有限群自同构群的p^mq^n阶群和p^n阶群,统一和推广了Curran在1988年和Caranti与Scoppola在1990年的文章的所有结果。     

Solitary subgroups of Abelian groups

Since solitary subgroups of (infinite) Abelian groups are precisely the strictly invariant subgroups which are co-Hopfian (as groups), and strictly invariant subgroups turn out to be strongly invariant for large classes of Abelian groups we determine the solitary subgroups for these classes of groups.     

Subnormality in linear groups

This paper investigates subnormality and its generalizations in the universe of linear groups. Among other results, it is proved that in any periodic linear group serial subgroups are ascendant, while descendant subgroups are subnormal. Moreover, the join of subnormal subgroups of linear groups is studied.     

Conjugately Dense Subgroups of Locally Finite Chevalley Groups of Lie Rank 1

Of interest are the subgroups of various groups which have nonempty intersection with each class of conjugate elements of the group under study. We call these subgroups conjugately dense and study Neumann's problem of describing them in the Chevalley groups over a field. The main theorem lists all conjugately dense subgroups of the Chevalley groups of Lie rank 1 over a locally finite field.     

Finite non-solvable groups in which the normalizer of every nonnormal cyclic subgroup is maximal

It is well known that the normality of subgroups plays an important part in the research of group theory. So it is reasonable to investigate the structure of a group by using normalizers of some kind of subgroups. In this paper we mainly investigate the structure of non-solvable groups in which the normalizer of every non-normal cyclic subgroup is a maximal subgroup, and finally the classification for this kind of groups is given.     

Representations of Parabolic and Borel Subgroups

We demonstrate a relationships between the representation theory of Borel subgroups and parabolic subgroups of general linear groups. In particular, we show that the representations of Borel subgroups could be computed from representations of certain maximal parabolic subgroups.     

A criterion for subnormality of subgroups in finite groups

Based on Wielandt’s criterion for subnormality of subgroups in finite groups, we study 2-maximal subgroups of finite groups and present another subnormality criterion in finite solvable groups.     

关于格序群的极大素子群

研究了格序群的极大素子群的性质以及由素子群根系确定的几种格序群类的结构。     

On p-nilpotency of finite groups with some subgroups π-quasinormally embedded

Summary A subgroup H of a group G is said to be π-quasinormal in G if it permutes with every Sylow subgroup of G, and H is said to be π-quasinormally embedded in G if for each prime dividing the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroups of G. We characterize p-nilpotentcy of finite groups with the assumption that some maximal subgroups, 2-maximal subgroups, minimal subgroups and 2-minimal subgroups are π-quasinormally embedded, respectively.     

Finite groups with some ss-quasinormal and c-normal subgroups

Let ℱ be a saturated formation containing the class of supersolvable groups. In this paper, we use c-normal subgroups and ss-quasinormal subgroups to give criteria for a group to belong to ℱ.