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1.
引入弱SS-半置换子群的概念,介绍了弱SS-半置换子群的性质,结合有限群G的极小于群的弱SS-半置换性,并结合C-正规性来讨论有限群的超可解性及幂零性,得到了有限群超可解及幂零的若干充分或充要条件,同时推广了某些著名结果. 相似文献
2.
众所周知,有限群的两个幂零子群的积不一定是幂零的.本文研究了Engel条件对两个幂零子群的影响,得到两个幂零子群的积为幂零群的几个充分条件。 相似文献
3.
《数学的实践与认识》2019,(24)
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. 相似文献
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设$G$为一个有限群, $H$是$G$的一个子群. 称$H$在$G$中是$s$-半置换的若对$G$的任意Sylow $p$-子群$G_p$, $HG_p=G_pH$, 其中$(p, |H|)= 1$,这里$p$是整除$G$的阶一个素数.通过假设$G$的一些子群是$s$-半置换的, 我们给出了$p$-幂零群的一个判定准则. 我们的结果推广了著名的Burnside $p$-幂零群准则. 相似文献
6.
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. 相似文献
7.
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).本文利用Sylow子群的2-极大子群的s-半置换性得到有限群为p-幂零群的一些充分条件. 相似文献
8.
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. 相似文献
9.
郭文彬 《数学年刊A辑(中文版)》2004,(2)
一个有限非幂零群G称为PN-群,如果NC(P)是幂零的,对于每个素数p和每个满足PZ∞(G)的非正规子群p-子群P.本文将给出可解PN-群的结构和一些特征定理. 相似文献
10.
具有幂零局部子群的有限群 总被引:3,自引:0,他引:3
一个有限非幂零群G称为PN-群,如果NG(P)是幂零的,对于每个素数p和每个满足P(∈)Z∞(G)的非正规子群p-子群P.本文将给出可解PN-群的结构和一些特征定理. 相似文献
11.
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. 相似文献
12.
Yuemei Mao & Xiaojian Ma 《数学研究》2016,49(1):50-56
Let $\mathfrak{F}$ be a non-empty formation of groups, $\tau$ a subgroup functor and $H$ a $p$-subgroup of a finite group $G.$ Let $\overline{G}=G/H_G$ and $\overline{H} =H/H_G.$ We say that $H$ is $\mathfrak{F}_\tau$-$s$-supplemented in $G$ if for some subgroup $\overline{T}$ and some $\tau$-subgroup $\overline{S}$ of $\overline{G}$ contained
in $\overline{H},$ $\overline{H}\overline{T}$ is subnormal in $\overline{G}$ and $\overline{H} ∩ \overline{T} ≤ \overline{S}Z_{\mathfrak{F}}(\overline{G}).$ In this paper, we investigate the
influence of $\mathfrak{F}_\tau$-$s$-supplemented subgroups on the structure of finite groups. Some
new characterizations about solubility of finite groups are obtained. 相似文献
13.
We establish the solvability of each finite group whose every proper nonmaximal subgroup lies in some subgroup of prime index. 相似文献
14.
假定H是有限群G的一个子群.如果对于|H|的每个素因子p,H的一个Sylow p-子群也是G的某个s-可换子群的Sylow p-子群,则称H为G的s-可换嵌入子群;如果存在G的子群T使得G=HT并且H∩T≤HG,其中HG为群G含于H的最大的正规子群,则称H为G的c-可补子群;如果存在G的子群T使得G=HT并且H∩T≤Hse,其中Hse为群G含于H的一个s-可换嵌入子群,则称H为G的弱s-可补嵌入子群.本文研究弱s-可补嵌入子群对有限群结构的影响.某些新的结论被进一步推广. 相似文献
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本文研究了一类2nm(m为奇数)阶有限群的构造,利用解数论同余方程的方法和群的扩张理论等知识,得到了具有奇数m阶循环正规子群、其补子群为循环群的2nm阶有限群的构造及相关的计数定理. 相似文献
17.
A non-nilpotent finite group whose proper subgroups are all nilpotent is called a Schmidt group. A subgroup A is said to be
seminormal in a group G if there exists a subgroup B such that G = AB and AB1 is a proper subgroup of G, for every proper subgroup B1 of B. Groups that contain seminormal Schmidt subgroups of even order are considered. In particular, we prove that a finite
group is solvable if all Schmidt {2, 3}-subgroups and all 5-closed {2, 5}-Schmidt subgroups of the group are seminormal; the
classification of finite groups is not used in so doing. Examples of groups are furnished which show that no one of the requirements
imposed on the groups is unnecessary.
Supported by BelFBR grant Nos. F05-341 and F06MS-017.
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Translated from Algebra i Logika, Vol. 46, No. 4, pp. 448–458, July–August, 2007. 相似文献
18.
We say that a subgroup H of a finite group G is solitary (respectively, normal solitary) when it is a subgroup (respectively, normal subgroup) of G such that no other subgroup (respectively, normal subgroup) of G is isomorphic to H. A normal subgroup N of a group G is said to be quotient solitary when no other normal subgroup K of G gives a quotient isomorphic to G/N. We show some new results about lattice properties of these subgroups and their relation with classes of groups and present examples showing a negative answer to some questions about these subgroups. 相似文献
19.
Suppose that G is a finite group and H is a subgroup of G . H is said to be s -permutably embedded in G if for each prime p dividing |H |, a Sylow p -subgroup of H is also a Sylow p -subgroup of some s -permutable subgroup of G ; H is called weakly s -permutably embedded in G if there are a subnormal subgroup T of G and an s -permutably embedded subgroup Hse of G contained in H such that G = HT and H ∩T ≤H se . In this paper, we continue the work of [Comm. Algebra, 2009, 37: 1086-1097] to study the influence of the weakly s -permutably embedded subgroups on the structure of finite groups, and we extend some recent results. 相似文献
20.
Victor S. Monakhov 《代数通讯》2020,48(1):93-100
AbstractA subgroup H of a finite group G is said to be Hall subnormally embedded in G if there is a subnormal subgroup N of G such that H is a Hall subgroup of N. A Schmidt group is a finite non-nilpotent group whose all proper subgroups are nilpotent. We prove the nilpotency of the second derived subgroup of a finite group in which each Schmidt subgroup is Hall subnormally embedded. 相似文献