共查询到19条相似文献,搜索用时 640 毫秒
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本文用有限单群分类定理解决了 E.Artin 所提出的如下问题:定出所有Sylow 子群的阶大于 g~(1/3)(g-|G|)的有限单群 G. 相似文献
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用阶刻划单群及有关课题 总被引:4,自引:0,他引:4
“群的阶”与“元的阶”是群论的两个最基本的概念,但它们在群的研究中起着重要的作用。 1902年W.Burnside提出如下著名的问题:若群G为有限生成,G中元的阶均为有限,G的阶是否有限?虽然Burnside的问题已由Golod给出了否定的答案,但它突出了“元的阶”在群的结构中的作用。 相似文献
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考察元素的阶如何影响有限群的结构是群论中的一个重要课题.本文研究存在一个正规子群N,N外的元素都是素数阶元的有阶群.主要利用熟知的Thompson的一个定理,获得了这样的有限群. 相似文献
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非正规极大子群同阶类类数=2的有限群 总被引:6,自引:2,他引:4
本文利用有限单群分类定理证明了下述定理:如果有限非可解群G恰有2个非正规极大子群同阶类,那么G/S(G)?PSL(2,7),这里S(G)表示G的最大可解正规子群。 相似文献
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能表示成四个真子群并的有限群 总被引:1,自引:1,他引:0
本文研究了子群覆盖问题.利用计算子群阶的方法,给出了能表示成p+1或p+2个真子群并的有限群G的结构,这里p是群G阶的最小素因子,从而推广了文献[1]中的结果. 相似文献
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本文根据有限Abel群G的自同构群A(G)的阶研究了群G的构造.利用有限交换群的一些性质,经过详细的理论推导,获得了|A(G)|=26p2(p为奇素数)的有限Abel群G的全部类型. 相似文献
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李学文 《数学的实践与认识》2005,35(8):233-238
群G关于S的有向Cayley图X=Cay(G,S)称为pk阶有向循环图,若G是pk阶循环群.利用有限群论和图论的较深刻的结果,对p2阶弧传递(有向)循环图的正规性条件进行了讨论,证明了任一p2阶弧传递(有向)循环图是正规的当且仅当(|Aut(G,S)|,p)=1. 相似文献
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Yoav Segev 《Israel Journal of Mathematics》1993,82(1-3):381-394
In this paper we develop some homological techniques to obtain fixed points for groups acting on finite Z-acyclic complexes.
In particular we show that if a groupG acts on a finite 2-dimensional acyclic simplicial complexD, then the fixed point set ofG onD is either empty or acyclic. We supply some machinery for determining which of the two cases occurs. The Feit-Thompson Odd
Order Theorem is used in obtaining this result.
This paper is dedicated to Prof. John G. Thompson on the occasion of receiving the Wolf Prize, 1992
This work was partially supported by BSF 88-00164. 相似文献
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In this paper, we deal mainly with the following problem: if every 2-maximal subgroup of a Sylow p-subgroup of a finite group G is S-seminormal in G, what conditions force G to be p-nilpotent? As an application of main results, some sufficient conditions for finite nilpotent groups and finite supersolvable groups are obtained. 相似文献
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A Cayley graph Γ=Cay(G,S)is said to be normal if G is normal in Aut Γ.In this paper,we investigate the normality problem of the connected 11-valent symmetric Cayley graphs Γ of finite nonabelian simple groups G,where the vertex stabilizer Av is soluble for A=Aut Γ and v ∈ VΓ.We prove that either Γ is normal or G=A5,A10,A54,A274,A549 or A1099.Further,11-valent symmetric nonnormal Cayley graphs of A5,A54 and A274 are constructed.This provides some more examples of nonnormal 11-valent symmetric Cayley graphs of finite nonabelian simple groups after the first graph of this kind(of valency 11)was constructed by Fang,Ma and Wang in 2011. 相似文献
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Bi-Cayley图的一些代数性质 总被引:1,自引:0,他引:1
设G是一个有限群,S是G的一个子集,Bi-Cayley图BC(G,S)是一个二部图:其顶点集为G×{0,1},而边集为{{(g,0),(sg,1)}:g∈G,s∈S}.本文研究了有限阿贝尔群G上的Cayley图D(G,S)和Bi-Calyley图BC(G,S)之间特征值的关系,并由此得到循环群上的Bi-Cayley图的特征值.继而得到生成树数的一些渐进性定理. 相似文献
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In this paper we continue the investigation of centralizer near-rings C(S;G) where S is a semigroup of endomorphisms of the
group G. We consider two situations. In Part I we take G=Sx for some x∈G and in Part II we take S to be a union of groups.
In each case we study the structure of C(S;G).
Dedicated to T. Tamura on his 65th Birthday 相似文献
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Michael Aschbacher 《Israel Journal of Mathematics》1993,82(1-3):1-43
We investigate the simple connectivity ofp-subgroup complexes of finite groups.
To John Thompson on the occasion of his receipt of the Wolf Prize
This work was partially supported by NSF DMS-8721480 and NSA MDA90-88-H-2032. 相似文献
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We determine the structure of finitely generated residually finite groups in which the number of subgroups of each finite
indexn is bounded by a fixed power ofn.
To John Thompson, an inspiration to group theory, on his being awarded the Wolf Prize
Partially supported by BSF and GIF grants.
Partially supported by a BSF grant. 相似文献
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Mingchun XU 《Frontiers of Mathematics in China》2013,8(5):1227-1236
For a finite group G, it is denoted by N(G) the set of conjugacy class sizes of G. In 1980s, J. G. Thompson posed the following conjecture: if L is a finite nonabelian simple group, G is a finite group with trivial center, and N(G) = N(L), then L and G are isomorphic. In this paper, it is proved that Thompson’s conjecture is true for the alternating group A 22 with connected prime graph. 相似文献
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Let p be an odd prime and S a finite p-group. B. Oliver’s conjecture arises from an open problem in the theory of p-local finite groups. It is the claim that a certain characteristic subgroup
\mathfrakX(S){\mathfrak{X}(S)} of S always contains the Thompson subgroup. In previous work the first two authors and M. Lilienthal recast Oliver’s conjecture
as a statement about the representation theory of the factor group
S/\mathfrakX(S){S/\mathfrak{X}(S)}. We now verify the conjecture for a wide variety of groups
S/\mathfrakX(S){S/\mathfrak{X}(S)}. 相似文献