共查询到20条相似文献,搜索用时 46 毫秒
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对称群的一个特征性质 总被引:1,自引:0,他引:1
设G为有限群,∑_n为n次对称群,本文证明了:G≌∑_n当且仅当|G|=|∑_n|且Π_e(G)=Π_e(∑_n),此处Π_e(G)为G中元的阶的集合。 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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本文讨论含指数为素数幂的超可解子群的有限群的结构.首先得到具有这种性质的非Abel有限单群的完全分类定理.其次给出了这类群是可解群和超可解群的若干充分条件. 相似文献
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设G是有限群,H(?)G。如果H≌~2B_2(q)或H≌~2G_2(q)或H≌PSU(3,q),则G不与任何射影平面的点传递直射群同均。本文对以下问题给出了一般方法:证明以某些几乎单群为点传递自同构群的线性空间不是射影平面。 相似文献
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Hereditary Upper Radical Properties and Dual Supplementing Radicals of Hereditary Radicals of Groups
One aim of this paper is to prove that for any hereditary radical property 𝒫, there exists a radical property 𝒫′ supplementing 𝒫. Certain hereditary upper radical properties of groups are constructed, and some of them are applied to formulate the necessary and sufficient condition for a hereditary radical 𝒫 and its supplementing radical 𝒫′ forming a dual pair. 相似文献
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《Journal of Algebra》2002,247(2):692-702
An associative ring R, not necessarily with an identity, is called radical if it coincides with its Jacobson radical, which means that the set of all elements of R forms a group denoted by R∘ under the circle operation r ∘ s = r + s + rs on R. It is proved that every radical ring R whose adjoint group R∘ is soluble must be Lie-soluble. Moreover, if the commutator factor group of R∘ has finite torsion-free rank, then R is locally nilpotent. 相似文献
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The notion of PI-representable groups is introduced; these are subgroups of invertible elements of a PI-algebra over a field. It is shown that a PI-representable group has a largest locally solvable normal subgroup, and this subgroup coincides with the prime radical of the group. The prime radical of a finitely generated PI-representable group is solvable. The class of PI-representable groups is a generalization of the class of linear groups because in the groups of the former class the largest locally solvable normal subgroup can be not solvable. 相似文献
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Roundness of metric spaces was introduced by Per Enflo as a tool to study uniform structures of linear topological spaces.
The present paper investigates geometric and topological properties detected by the roundness of general metric spaces. In
particular, we show that geodesic spaces of roundness 2 are contractible, and that a compact Riemannian manifold with roundness
>1 must be simply connected. We then focus our investigation on Cayley graphs of finitely generated groups. One of our main
results is that every Cayley graph of a free Abelian group on ⩾ 2 generators has roundness =1. We show that if a group has
no Cayley graph of roundness =1, then it must be a torsion group with every element of order 2,3,5, or 7
Partially supported by a Canisius College Summer Research Grant 相似文献
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Siberian Mathematical Journal - Saturation and the related concept of a saturating set are among the finiteness conditions for infinite groups. Saturation is applied to studying periodic... 相似文献
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In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups. 相似文献
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Bernd Ackermann 《代数通讯》2013,41(11):3751-3758
In this article we give a branching rule for Harish–Chandra restriction from the general linear group Gl n (q) to the Levi subgroup Gl n?1(q) × Gl1(q) in the case of the unipotent block. 相似文献
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J. L. Alperin 《代数通讯》2013,41(3):889-891
Let U(n,q) be the group of upper uni-triangular matrices in GL(n,q), the n-dimensional general linear group over the field of q elements. The number of U(n,q)-conjugacy classes in GL(n,q) is, as a function of q, for fixed n, a polynomial in q with integral coefficients. 相似文献
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Sheu T. L. 《Journal of Algebra》1993,160(2)
In a recent paper, A. Bialostocki (Israel J. Math.41 (1982), 261-273) has defined a nilpotent injector in an arbitrary finite group G to be a maximal nilpotent subgroup of G, containing a subgroup H of G of maximal order satisfying class (H) ≤2. In the present paper, the author determines the nilpotent injectors of GL(n, q) and shows that they form a unique conjugacy class of subgroups of GL(n, q). It is also proved that if n ≠ 2 or n = 2 and q ≠ 9 is not a Fermat prime >3, then the nilpotent injectors of GL(n, q) are the nilpotent subgroups of maximal order. 相似文献