共查询到19条相似文献,搜索用时 62 毫秒
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群 G 的一个子群 H 称为在 G 中具有半覆盖远离性,如果存在 G 的一个主群列1=G_0< G_1<…<G_1=G,使得对每一 i=1,…,l 或者 H 覆盖 G_j/G_(j-1)或者 H 远离 G_j/G_(j-1).本文证明了予群的半覆盖远离性是子群 C-正规性和子群的覆盖远离性之推广.进一步应用极大子群和 Sylow 子群给出了有限群为可解群的一些特征. 相似文献
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某些子群是半正规的有限群 总被引:6,自引:0,他引:6
本文旨在考查极大子群对有限群结构的影响.首先给出了商群超可解的群是超可解群的若干充分条件;其次考查了n-极大子群对有限群的可解性及超可解性的影响 相似文献
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半正规n-极大子群对有限群结构的影响 总被引:1,自引:0,他引:1
设△↓n(G)为有限群G的n次极大子群的全体。1.若△↓4(G)中的子群均在G中半正规,则下述结论之一成立:(1)G是可解群;(2)G/φ(G)=A5,(3)G/φ(G)=PSL(2,13);(4)G/φ(G)=PSL(2,p),满足p=4p1 1=6p2-1,这里p1≥43,p2≥29;(5)G/φ(G)=PSL(2,p),满足p=6p1 1=4p2-1,这里p1≥7,p2≥11.2。2.设3不属于π(G),若△↓(G)中的子群均在G中半正规,则G是可解群,或G/φ(G)=Sz(2^3). 相似文献
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Matthew F. Ragland 《代数通讯》2013,41(10):3242-3252
A group G is called a Hall𝒳-group if G possesses a nilpotent normal subgroup N such that G/N′ is an 𝒳-group. A group G is called an 𝒳o-group if G/Φ(G) is an 𝒳-group. The aim of this article is to study finite solvable Hall𝒳-groups and 𝒳o-groups for the classes of groups 𝒯, 𝒫𝒯, and 𝒫𝒮𝒯. Here 𝒯, 𝒫𝒯, and 𝒫𝒮𝒯 denote, respectively, the classes of groups in which normality, permutability, and Sylow-permutability are transitive relations. Finite solvable 𝒯-groups, 𝒫𝒯-groups, and 𝒫𝒮𝒯-groups were globally characterized, respectively, in Gaschütz (1957), Zacher (1964), and Agrawal (1975). Here we arrive at similar characterizations for finite solvable Hall𝒳-groups and 𝒳o-groups where 𝒳 ∈ {𝒯, 𝒫𝒯, 𝒫𝒮𝒯}. A key result aiding in the characterization of these groups is their possession of a nilpotent residual which is a nilpotent Hall subgroup of odd order. The main result arrived at is Hall𝒫𝒮𝒯 = 𝒯o for finite solvable groups. 相似文献
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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
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
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Lehmer问题的两个推广 总被引:1,自引:0,他引:1
设素数P>2,整数C与P互素.对任意整数1≤a≤P-1,存在惟一的整数 1≤b≤P-1满足ab≡c mod P.Lehmer建议我们研究a与b的奇偶性不同的情形.本文给出了这一问题的两个推广,并获得了两个有趣的混合均值公式. 相似文献
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Gavin Brown William Moran Andrew D. Pollington 《Journal of Fourier Analysis and Applications》2002,8(5):427-442
The aim of this article is to prove the two-dimensional case of Wolfgang Schmidt's conjecture for normality with respect to matrices. Specifically we show that if S and T are two by two almost integer ergodic matrices, then normality with respect to S implies normality with respect to T if and only if Sp = Tq for some positive integers p and q. 相似文献
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文献[1]中,我们用有关鞅的中心极限定理,证明了系统辨识中LS估计的渐近正态性。然而[1]中的条件是苛刻的。本文利用Mcleish的相依变量的中心极限定理改进了[1]的结果。 相似文献
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V. A. Ustimenko 《Acta Appl Math》1998,52(1-3):223-238
Investigations of homogeneous varieties T=(G:P) of all cosets of finite Coxeter or Chevalley groups G by their maximal parabolic subgroups P had been conducted at the Kalunin seminar at Kiev State University since the 1970s, as were investigations of their corresponding permutation groups, geometries and association schemes.In I. A. Faradev et al. (eds), Investigations in Algebraic Theory of Combinatorial Objects (Kluwer Acad. Publ., 1994), one can find some results on the investigation of noncomplete Galois correspondence between fusion schemes of the orbital scheme for (G,T) and overgroups of (G,T), as well as calculations of the intersectional indices of the Hecke algebra of (G,T). We will discuss additional results on this topic and consider questions related to the following problems: embeddings of varieties (G:P) into the Lie algebra corresponding to Chevalley group G; interpretations of Lie geometries, small Schubert cells, connections between the geometry of G and its associated Weyl geometry in terms of linear algebra, and applications of these problems to calculations performed in Lie geometries and association schemes; constructions of geometric objects arising from Kac–Moody Lie algebras and superalgebras, and applications of these constructions to investigations of graphs of large girth and large size. 相似文献
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本文是在日本数学家Kemoto 1993年所作的关于一个GO-空间(广义线性序空间)和一个正则不可数基数乘积正规性的结果的基础上作了进一步的推广,得到了两个GO-空间乘积的正规性的一个更一般的结果. 相似文献