关于有限群的p-幂零性

设G是一个有限群,p是|G|的最小素因子,主要研究了G的p阶或4阶循环子群的S-半置换性和NE-性对G的结构的影响,继而证明p阶或4阶循环子群的S-半置换性和NE-性与G的p-幂零性之间的关系.在此基础上,将上述结果推广到G=AB的情形,其中A和B是G的次正规子群,或者A和B完全置换.     

具有p-幂零s-补子群的有限群（英文）

有限群G的子群H叫做F-s-补子群,若存在G的一个子群K使得G=HK且K/(K∩H_G)∈F,其中F是一个群类.本论文利用p-幂零s-补子群得到了关于有限群为p-幂零群的一些新成果.     

p-幂零群和p-闭群的若干充分条件

交换子群的中心化子和正规化子对有限群的结构有很强的控制作用,本文主要通过考虑某些交换子群的中心化子一致于正规化子,得到了p-幂零群和p-闭群的若干充分条件.     

弱s-拟正规子群对有限群的p-幂零性的影响

群G的子群H称为G的弱s-拟正规子群,若G有次正规子群T,使得G=HT且H ∩T≤HsG,其中HsG是包含在H中的G的最大的s-拟正规子群.本文利用Sylow p-子群的极大子群的弱s-拟正规性得到有限群为p-幂零群的一些充分条件,并给出Schur-Zassenhaus定理的一种推广.     

弱ss-置换子群与有限群的p-幂零性

称群G的一个子群H在G中弱ss-置换的,如果存在G的一个次正规子群T和包含在H中的G的一个ss-置换子群Hss使得G=HT且H∩T≤Hss．利用子群的弱ss-置换性得到了有限p-幂零群的一些新的刻画．     

有限群的c-半置换子群

研究了有限群的结构问题,利用子群c-半置换和完全c-半置换的定义和性质,通过对有限群sylow子群的2-极大子群的研究,获得了有限群幂零、p-幂零的充分条件和另外两个决定群结构的充要条件.     

有限群的弱正规子群与p-幂零性

研究了p2阶子群以及一般的pk阶子群为弱正规子群时有限群G的结构.给出了有限群为p-幂零群以及超可解群的一些条件.     

有限群的p-幂零性和极小子群

从有限群构造的角度来看,p-幂零群和p-可分解群很相似,前者是p-群和p'-群的半直积,后者是p-群和P'-群的直积.有限群G的p-可分解剩余是P(G)=∩{H|H(⊿) G,而且G/H是p-可分解}.通过观察p-可分解剩余和极小子群的性质得到了几个关于p-幂零的充要条件.     

s-半置换子群对有限群的p-超可解性的影响

群G的子群H称为半置换的,若对任意的K≤G,只要（｜H｜,｜K｜）=1,就有HK=KH．H称为s-半置换的,若对任意的p｜｜G｜,只要（p,｜H｜）=1,就有PH=HP,其中P∈Sylp（G）．本文研究Sylow子群的极大子群及极小子群的s-半置换性对有限群的p-超可解性的影响．     

关于有限群的p-超可解性

本文研究了有限群的p-超可解性,利用子群的s-条件置换性及Sylow子群的极大子群对有限群结构的影响,得到了一个群为p-超可解群的一些充分必要条件.     

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.     

Some Results on p-Nilpotence and Supersolvability of Finite Groups

Let G be a finite group. A subgroup K of a group G is called an ?-subgroup of G if N _G (K) ∩ K ^x  ≦ K for all x ? G. The set of all ?-subgroups of G will be denoted by ?(G). Let P be a nontrivial p-group. A chain of subgroups 1 = P ₀ ? P ₁ ? ··· ? P _n  = P is called a maximal chain of P provided that |P _i : P _i?1| = p, i = 1, 2, ···, n. A nontrivial p-subgroup P of G is called weakly supersolvably embedded in G if P has a maximal chain 1 = P ₀ ? P ₁ ? ··· ? P _i  ? ··· ? P _n  = P such that P _i  ? ?(G) for i = 1, 2, ···, n. Using the concept of weakly supersolvably embedded, we obtain new characterizations of p-nilpotent and supersolvable finite groups.     

p-Fitting子群的CAP-嵌入子群

群G的子群H称为G的CAP-嵌入子群,如果对于|H|的每个素因子p,存在G的某个CAP-子群K,使得H的某个Sylow p-子群也是K的一个Sylowp-子群.本文通过假定G的p-Fitting子群F_p(G)的某个Sylow p-子群的每个极大子群是G的CAP-嵌入子群,得到一些新的结果.     

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.     

New characterizations of finite supersoluble groups

Let A be a subgroup of a group G and X a nonempty subset of G.A is called an X- semipermutable subgroup of G if A has a supplement T in G such that for every subgroup T_1 of T there exists an clement x∈X such that AT_i~x=T_i~xA.On the basis of this concept we obtain some new characterizations of finite supersoluble groups.     

On SS-quasinormal subgroups and the structure of finite groups

A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure of a group under the assumption that every subgroup with order pm of a Sylow p-subgroup P of G is SS-quasinormal in G for a fixed positive integer m. Some interesting results related to the p-nilpotency and supersolvability of a finite group are obtained. For example, we prove that G is p-nilpo...     

On Finite Groups with Some Semi Cover-Avoiding Subgroups

A subgroup H of a finite group G is said to have the semi-cover-avoiding property in G if there is a chief series of G such that H covers or avoids every chief factor of the series. In this paper, some new results are obtained based on the assumption that some subgroups have the semi-cover-avoiding property in the group.     

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.