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1.
有限群G叫(q)-群,如果G中每个次正规子群均为拟正规子群,群G叫Eq-群,若G中每个子群在G中拟正规或自正规,有限群G叫内Eq-群,如果G本身不是Eq-群,但G的每个真子群是Eq-群,本文确定了Eq-群的结构与内Eq-群的分类.  相似文献   

2.
生成Fuzzy子群   总被引:7,自引:2,他引:5  
群X上含Fuzzy子集μ的最小Fuzzy子群称是μ的生成Fuzzy子群,记为[μ],本文一方面从解析要求出发给出了从μ生成[μ]的生成公式,另一方面又蛤出了用对水平集集{μ_λ}的等价分类来直接构成[μ]的过程,还讨论了值城[μ](X)和μ(X)之间的各种内在联系,以及水平集[μ_λ]和[μ]_λ之间的关系。  相似文献   

3.
某些幂零子群与可解性   总被引:2,自引:1,他引:1  
韦华全  班桂宁 《数学杂志》1999,19(3):257-262
本文利用某些幂子群的半正规性,讨论有限群的可解性,所得结果统一推广了王品超、赵耀庆的若干结果。  相似文献   

4.
本文对[1]中关于极大上下对的公开问题给出否定的回答并构造了例子说明[2]中命题2.1证明过程中的错误;研究了saturated子群的构造,得到了任意ι-群的正交子集生成的saturated子群以及投射ι—群的任一子集生成的saturated子群的具体形式.  相似文献   

5.
二次极大子群中2阶及4阶循环子群拟中心的有限群   总被引:1,自引:0,他引:1  
钟祥贵 《数学杂志》2004,24(3):245-248
本文讨论2阶及4阶循环子群对群结构的影响.证明二次极大子群中2阶及4阶循环子群拟中心的有限群G同构于下列群之一:(1)G为2-闭群;(2)G为2-幂零群;(3)G≌S,;(4)G=PQ.其中P为2^4阶广义四元数群,Q≌C3;(5)G≌A5或SL(2,5).  相似文献   

6.
与正规性相关的各种子群之间的关系   总被引:5,自引:0,他引:5  
张勤海  王丽芳 《数学研究》2003,36(4):412-417
本讨论了正规子群,拟正规子群,s-拟正规子群,半正规子群,c-正规子群,次正规子群,共轭置换子群,半置换子群,s-半置换子群这九种子群之间的关系。  相似文献   

7.
黎先华 《数学杂志》1995,15(2):182-186
如果有限群G的每个极大子群的指数和质因子个数都小于或等于n,则称G为n-因指数群。本文用单群分类定理证明了。  相似文献   

8.
有限群G的子群H称为G的BNA子群,若对任意的x∈G有H^(x)=H或x∈.若有限群G的所有素数阶和4阶循环子群都是G的BNA子群,则称G为CBNA群.本文主要刻画CBNA群的结构,并且给出所有真子群都是CBNA群的完全分类.  相似文献   

9.
10.
对各种类型的不可约根系,讨论了其Weyl群一类子群的极大性。  相似文献   

11.
A Note on c-Supplemented Subgroups of Finite Groups   总被引:1,自引:0,他引:1  
A. A. Heliel 《代数通讯》2013,41(4):1650-1656
A subgroup H of a finite group G is said to be c-supplemented in G if there exists a subgroup K of G such that G = HK and HK is contained in H G , where H G is the largest normal subgroup of G contained in H. In this article, we prove that G is solvable if every subgroup of prime odd order of G is c-supplemented in G. Moreover, we prove that G is solvable if and only if every Sylow subgroup of odd order of G is c-supplemented in G. These results improve and extend the classical results of Hall's articles of (1937) and the recent results of Ballester-Bolinches and Guo's article of (1999), Ballester-Bolinches et al.'s article of (2000), and Asaad and Ramadan's article of (2008).  相似文献   

12.
Let H be a subgroup of a finite group G. H is nearly SS-embedded in G if there exists an S-quasinormal subgroup K of G, such that HK is S-quasinormal in G and H ∩ K ≤ HseG, where HseG is the subgroup of H, generated by all those subgroups of H which are S-quasinormally embedded in G. In this paper, the authors investigate the influence of nearly SS-embedded subgroups on the structure of finite groups.  相似文献   

13.
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.  相似文献   

14.
郭鹏飞 《数学研究》2006,39(1):83-88
考查了次正规子群对有限群结构的影响,得到有限群可解的若干充分条件和超可解的一个充分条件.  相似文献   

15.
Khaled A. Al-Sharo 《代数通讯》2013,41(10):3690-3703
Let G be a finite group and H ≤ G. The subgroup H is called: S-permutable in G if HP = PH for all Sylow subgroups P of G; S-permutably embedded in G if each Sylow subgroup of H is also a Sylow subgroup of some S-permutable subgroup of G.

Let H be a subgroup of a group G. Then we say that H is SQ-supplemented in G if G has a subgroup T and an S-permutably embedded subgroup C ≤ H such that HT = G and TH ≤ C.

We study the structure of G under the assumption that some subgroups of G are SQ-supplemented in G. Some known results are generalized.  相似文献   

16.
Tests for π-solvability of a finite group with seminormal Hall π-subgroup are established and the nilpotency of the third commutator subgroup of any group with seminormal noncyclic Sylow subgroups is proved.  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. __________ Translated from Algebra i Logika, Vol. 46, No. 4, pp. 448–458, July–August, 2007.  相似文献   

18.
Xinjian Zhang 《代数通讯》2017,45(11):4971-4973
In this paper, we studied the supersolvability of the product of two subgroups and got a generalization of Baer’s theorem.  相似文献   

19.
Hongfei Pan 《代数通讯》2018,46(7):3198-3204
We study the supersolvability of finite groups and the nilpotent length of finite solvable groups under the assumption that all their exactly n-minimal subgroups are S-permutable, where n is an arbitrary integer.  相似文献   

20.
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