On S~i-quasinormal Subgroups

The objective of this paper is to invertigate the influence of maximal subgroups on the structure of a finite group.We introduce a concept of "normality" based on the permuting of certain subgroups.This concept leads to a generalization of Asaad and Shaalan's result.     

Witt指数n的有限正交单群的一个新刻画

运用有限单群分类定理,证明了有限群G同构于Witt指数n(其中除n为4,6,8,10,12,14,16外)的有限正交单群PΩ 2n(q),当且仅当(1)πe(G)=πe(PΩ 2n(q)),πe(G)表示G中元素的阶的集合,(2)ord(Snor(G))=ord(Snor(PΩ 2n(q))),ord(Snor(G))为G的Sylow子群的正规化子的阶之集合.在某种意义推进了施武杰教授的一个著名猜想.     

On sylowizers in finite <Emphasis Type="Italic">p</Emphasis>-soluble groups

In general, given a finite group G, a prime p and a p-subgroup R of G, the sylowizers of R in G are not conjugate. In this paper we afford some conditions to achieve the conjugation of the sylowizers of R in a p-soluble group G, among others

Finite groups with <Emphasis Type="Italic">C</Emphasis>-quasinormal subgroups

Consider some finite group G and a finite subgroup H of G. Say that H is c-quasinormal in G if G has a quasinormal subgroup T such that HT = G and T ∩ H is quasinormal in G. Given a noncyclic Sylow subgroup P of G, we fix some subgroup D such that 1 < |D| < | P| and study the structure of G under the assumption that all subgroups H of P of the same order as D, having no supersolvable supplement in G, are c-quasinormal in G.     

有限超可解群的置换乘积

群G的两个子群H和K称为可置换的,如果HK=KH.利用子群的可置换性,给出了两个超可解子群A和B的乘积仍为超可解群的一个判别准则.     

超可解群的两个判别准则

群G的子群H称为在G中弱s可补充的,如果G有子群K,使得HK=G且H∩K≤H;c．这里H;c是包含在H中的G的最大s置换子群．利用准素子群的弱s可补充性质,给出了超可解群的两个充分条件．     

准素子群的几乎s正规性对超中心的影响

设H是有限群G的子群,若存在G的正规子群K,使得HK G,且H∩K≤HsG,HsG是G的包含于H的最大s拟正规子群,则称H在G中几乎s正规.本文利用某些准素子群的几乎s正规性来研究有限群的FΦ超中心的构造.     

The generic character table of a Sylow p-subgroup of a finite Chevalley group of type D4

Let U be a Sylow p-subgroup of the finite Chevalley group of type D₄ over the field of q elements, where q is a power of a prime p. We describe a construction of the generic character table of U.     

准素子群的局部化性质对群结构的影响

已知H是群G的子群,若存在G的子群B,使得(1)G＝HB,(2)若H1/HG是H/HG的极大子群,则H1B＝BH1 Sylow子群的正规化子中,利用子群的弱M－可补性对有限群的结构进行探索,得到关于群p－幂零性以及包含超可解群系的饱和群系结构的一些结果.