关于有限群某些子群的X-半置换性

Let A be a subgroup of a group G and X a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we try to use the X-semipermutability of some subgroups to characterize the structure of finite groups.     

非平凡正规子群只有两种阶数的有限群

In this paper, we investigate the structure of the groups whose nontrivial normal subgroups have order two. Some properties of this kind of groups are obtained.     

所有子群皆交换或正规的有限群

本文研究所有子群皆交换或正规的有限群. 我们获得了非幂零的情形的一个特征刻画, 也给出了幂零情形的一些性质.     

A question on partial CAP-subgroups of finite groups

A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids every chief factor of the series.The structural impact of the partial cover and avoidance property of some distinguished subgroups of a group has been studied by many authors.However,there are still some open questions which deserve an answer.The purpose of the present paper is to give a complete answer to one of these questions.     

关于有限群的S-半置换子群

Let d be the smallest generator number of a finite p-group P and let Md（P） = {P1,...,Pd} be a set of maximal subgroups of P such that ∩di=1 Pi = Φ（P）. In this paper, we study the structure of a finite group G under the assumption that every member in Md（Gp） is S-semipermutable in G for each prime divisor p of ｜G｜ and a Sylow p-subgroup Gp of G.     

有限群的s-条件置换子群

如果对群G的任意Sylow子群T,存在一个元素x∈G,使得HTx=TxH,那么称群G的子群H在G中s-条件置换.利用s-条件置换子群给出了一些群的性质和结构.     

有限群的s-条件置换子群

如果对群G的任意Sylow子群T,存在一个元素x∈G,使得HT~x=T~xH,那么称群G的子群H在G中s-条件置换．利用s-条件置换子群给出了一些群的性质和结构．     

s-半置换子群对有限群结构的影响

称有限群G的子群H在G中s-半置换,如果H与G的每个Sylowp-子群可换,其中(p,|H|)=1.本文研究了s-半置换子群对有限群结构的影响..     

关于有限群的阶与其特征标的商

设Ｇ是有限群．Ｄ．Ｃｈｉｌｌａｇ和Ｍ．Ｈｅｒｚｏｇ曾考察过下述问题：商集合｛｜Ｇ｜／Ｘ（ｘ）｜Ｘ∈ＩＩｒ（Ｇ）｝上的某些算术条件如何影响群Ｇ本身的结构．本义继续研究这个问题．     

τ-拟置换子群对有限群结构的影响

群G的一个子群H称为τ-拟置换的,如果G有一个子群B满足G=N_G(H)B且HB=BH,同时对于B的Sylow q-子群Q,只要满足(|H|,q)=1但(|H|,|Q^G|)≠1,便有HQ=QH,其中q是|B|的任一素因子.研究了τ-拟置换子群对有限群结构的影响.应用极小阶反例的方法得到了群G是p-超可解群的一个新的判定,又利用群G的F-剩余子群G^F的性质以及群G的准素数子群的τ-拟置换性得到了群G的半直积结构     

The influence of s-conditionally permutable subgroups on finite groups

A subgroup H of a group G is called s-conditionally permutable in G if for every Sylow subgroup T of G there exists an element x ∈ G such that HTx = TxH. Using the concept of s-conditionally permutable subgroups, some new characterizations of finite groups are obtained and several interesting results are generalized.     

The Influence of Primitive Subgroups on the Structure of Finite Groups

A subgroup $H$ of a group $G$ is said to be primitive if it is a proper subgroup of the intersection of all subgroups of $G$ containing $H$ as its proper subgroup. The purpose of this note is to go further into the influence of primitive subgroups on the structure of finite groups. Some new results are obtained.     

Hall共轭嵌入子群对有限群结构的影响

设群G为有限群,日为G的子群.若对任意的g∈G,日为〈H,H~g〉的Hall子群,则称子群日为G的Hall共轭嵌入子群.利用Hall共轭嵌入子群得到有限群G分别为幂零群与超可解群的若干新的判定方法.     

关于CAP-子群的一点注记（英文）

对于有限群G的每一主因子H/K来说,若G的子群L满足LH=LK或者L∩H=L∩K,则称L是G的CAP-子群.本文通过假设G的每个非循环Sylow子群P有一个子群D使得1〈｜D｜〈｜P｜,且P的所有阶为｜D｜和2｜D｜（若P是非交换2-群且｜P∶D｜〉2）的子群H是G的CAP-子群,得到G为p-幂零群的一个结果.     

On SS-Quasinormal Subgroups of Finite Groups

A subgroup of a group G is said to be Sylow-quasinormal (S-quasinormal) in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be Supplement-Sylow-quasinormal (SS-quasinormal) in G if there is a supplement B of H to G such that H is permutable with every Sylow subgroup of B. In this article, we investigate the influence of SS-quasinormal of maximal or minimal subgroups of Sylow subgroups of the generalized Fitting subgroup of a finite group.     

The Influence of Weakly s-Supplemented Subgroups on the Structure of Finite Groups

Let G be a finite group. A subgroup H of G is said to be weakly s-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ H _{s G} , where H _{s G} is the subgroup of H generated by all those subgroups of H which are s-quasinormal in G. In this article, we investigate the structure of G under the assumption that some families of subgroups of G are weakly s-supplemented in G. Some recent results are generalized.     

弱 c- 可置换子群对有限群结构的影响

Guo和Chen在2010年引入了弱c-可置换子群的概念,并利用这种新的广义置换性质对有限群的结构给出了一些新的刻画.本文推广了上述文献中的两个主要结论,确定了极小子群为弱c-可置换子群的有限群的结构.     

具有弱$s$-置换嵌入子群的有限群

Let P be a Sylow p-subgroup of a group G with the smallest generator number d,where p is a prime.Denote by M_d(P) = {P_1,P_(2,...,)P_d} a set of maximal subgroups of P such that φ(P) = ∩_(n=1)~dP_n.In this paper,we investigate the structure of a finite group G under the assumption that the maximal subgroups in M_d(P) are weakly s-permutably embedded in G,some interesting results are obtained which generalize some recent results.Finally,we give some further results in terms of weakly s-permutably embedded subgroups.