共查询到20条相似文献,搜索用时 15 毫秒
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We study finite groups some of whose Schmidt subgroups (the minimal nonnilpotent subgroups) are subnormal. 相似文献
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如果群G有次正规子群K使HK⊿⊿G且H∩K⊿⊿G,那么子群H被称做群G的弱次正规子群.利用极大子群Sylow子群或Sylow子群正规化子的子群的弱次正规性得到了一些关于有限群的可解性结论. 相似文献
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Given a prime \( p \) and a partition \( \sigma=\{\{p\},\{p\}^{\prime}\} \) of the set of all primes, we describe the structure of the nonnilpotent finite groups whose every Schmidt subgroup is \( \sigma \)-subnormal.
相似文献5.
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Shi Rong LI 《数学学报(英文版)》2007,23(5):885-888
For any saturated formation F of finite groups containing all supersolvable groups, the groups in F are characterized by F-abnormal maximal subgroups. 相似文献
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Siberian Mathematical Journal - We study the influence of weakly subnormal and partially subnormal subgroups on the structure of a group $ G $ . In particular, we prove that a... 相似文献
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有限群的Fuzzy次正规子群与Fuzzy极大子群 总被引:1,自引:1,他引:1
本文研究了有限群的F次正规子群,得出了一个F子群是F次正规子群的充要条件,讨论了F次正规子群的一些重要性质。另外,本文还引入了有限群的F极大子群的概念,给出了F子群是F极大群的充要条件。最后,给出了三个定理,讨论了有限群G可解、超可解、幂零与G的F次正规子群、F极大子群之间的联系。 相似文献
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The following result is established. THEOREM. Let G be a periodic, residually finite group with allsubgroups sub-normal. Then G is nilpotent. The well-known groups of Heineken and Mohamed [1] show thatthe hypothesis of residual finiteness cannot be omitted here,while examples in [5] show that a residually finite group withall subgroups subnormal need not be nilpotent. The proof ofthe Theorem will use the results of Möhres that a groupwith all subgroups subnormal is soluble [3] and that a periodichypercentral group with all subgroups subnormal is nilpotent[4]. Borrowing an idea from [2], the plan is to construct certainsubgroups H and K that intersect trivially, and to show thatthe subnormality of both leads to a contradiction. 1991 MathematicsSubject Classification 20E15. 相似文献
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Manuel J. Alejandre A. Ballester-Bolinches M. C. Pedraza-Aguilera 《Journal of Algebra》2001,240(2):207
A finite group G is said to be a PST-group if every subnormal subgroup of G permutes with every Sylow subgroup of G. We shall discuss the normal structure of soluble PST-groups, mainly defining a local version of this concept. A deep study of the local structure turns out to be crucial for obtaining information about the global property. Moreover, a new approach to soluble PT-groups, i.e., soluble groups in which permutability is a transitive relation, follows naturally from our vision of PST-groups. Our techniques and results provide a unified point of view for T-groups, PT-groups, and PST-groups in the soluble universe, showing that the difference between these classes is quite simply their Sylow structure. 相似文献
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V. S. Monakhov 《Algebra and Logic》2004,43(4):230-237
We look at the structure of a soluble group G depending on the value of a function m(G)= max m
p
G), where m
p(G)=max{logp|G:M| | M< G, |G:M|=p
a}, p (G). Theorem 1 states that for a soluble group G, (1) r(G/ (G))= m(G); (2) d(G/ (G)) 1+ (m(G)) 3+m(G); (3) l
p(G) 1+t, where 2t-1<m
p(G) 2t. Here, (G) is the Frattini subgroup of G, and r(G), d(G), and l
p(G) are, respectively, the principal rank, the derived length, and the p-length of G. The maximum of derived lengths of completely reducible soluble subgroups of a general linear group GL(n,F) of degree n, where F is a field, is denoted by (n). The function m(G) allows us to establish the existence of a new class of conjugate subgroups in soluble groups. Namely, Theorem 2 maintains that for any natural k, every soluble group G contains a subgroup K possessing the following properties: (1) m(K); k; (2) if T and H are subgroups of G such that K T <max <max
H G then |H:T|=p
t for some prime p and for t>k. Moreover, every two subgroups of G enjoying (1) and (2) are mutually conjugate. 相似文献
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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 T ∩ H ≤ 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
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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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Let G be a finite group. We fix in every noncyclic Sylow subgroup P of G some subgroup D satisfying 1 < |D| < |P| and study the structure of G under the assumption that all subgroups H of P with |H| = |D| are c-normal in G. 相似文献
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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
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设$G$是有限群, $N(G)$为$G$的norm, 则$N(G)$是$G$的正规化G的每个子群的特征子群. 我们在下列条件之一下,研究了$G$的结构:1) Norm商群$G/N(G)$是循环群;2) Norm商群$G/N(G)$的所有Sylow子群都是循环群,特别地当$G/N(G)$的阶是无平方因子数时. 相似文献
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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. 相似文献