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最高阶元素个数不同的有限群 总被引:18,自引:0,他引:18
杨成 《数学年刊A辑(中文版)》1993,(5)
本文首先讨论了当群G的某r阶元素的集合M_(?)(G)只含两个元素时G的性质,然后给出了当群G的最高阶元素的集合M(G)只含两个元素时群G的一个刻划,最后得到了当|M(G)|为奇数或不大于4时,群G为超可解;当|M(G)|=2p,p为素数,G为可解群。 相似文献
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最高阶元素个数不同的有限群 总被引:7,自引:0,他引:7
杨成 《数学年刊B辑(英文版)》1993,(5)
本文首先讨论了当群 G 的某 r 阶元素的集合 M_r(G)只含两个元素时 G 的性质,然后给出了当群 G 的最高阶元素的集合 M(G)只含两个元素时群 G 的一个刻划,最后得到了当|M(G)|为奇数或不大于4时,群 G 为超可解;当|M(G)|=2p,p 为素数,G 为可解群. 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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最高阶元素个数为2p~2的有限群是可解群 总被引:8,自引:0,他引:8
姜友谊 《数学年刊A辑(中文版)》2000,(1)
本文讨论了最高阶元素个数 |M(G)|= 2P2 (为素数)的有限群,证明了群 G是可解群 相似文献
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本文给出了满足下面条件的有限可解群的分类存在某个元素,使得不同的不可约特征标在该元素上取不同的值. 相似文献
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本文给出了满足下面条件的有限可解群的分类:存在某个元素,使得不同的不可约特征标在该元素 上取不同的值. 相似文献
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Takao Satoh 《Journal of Pure and Applied Algebra》2007,211(2):547-565
In this paper, we compute the second homology groups of the automorphism group of a free group with coefficients in the abelianization of the free group and its dual group except for the 2-torsion part, using combinatorial group theory. 相似文献
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Christopher Thomas 《Journal of Pure and Applied Algebra》2005,195(2):211-224
In this article we give necessary and sufficient conditions for a given finite group of outer automorphisms to be induced by the action of a group of orientation-preserving homeomorphisms on the fundamental group of a punctured surface. When the group is abelian, necessary and sufficient conditions can also be given in the absence of orientability assumptions. These properties are formulated in terms of the finite automorphism groups which project into the given outer automorphism group: each non-trivial automorphism in any such group can fix at most a cyclic subgroup of the fundamental group. 相似文献
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HX群是由一个群向其幂集上提升的群结构.文[1]将HX群推广到一类特殊的格-原子格L上,称之为AHX群.本文研究了一类特殊的AHX群-拟L商群的同态与同构,获得与拟商群相类似的结果. 相似文献
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A pro-Lie group is a projective limit of a projective system of finite dimensional Lie groups. A prodiscrete group is a complete abelian topological group in which the open normal subgroups form a basis of the filter of identity neighborhoods. It is shown here that an abelian pro-Lie group is a product of (in general infinitely many) copies of the additive topological group of reals and of an abelian pro-Lie group of a special type; this last factor has a compact connected component, and a characteristic closed subgroup which is a union of all compact subgroups; the factor group modulo this subgroup is pro-discrete and free of nonsingleton compact subgroups. Accordingly, a connected abelian pro-Lie group is a product of a family of copies of the reals and a compact connected abelian group. A topological group is called compactly generated if it is algebraically generated by a compact subset, and a group is called almost connected if the factor group modulo its identity component is compact. It is further shown that a compactly generated abelian pro-Lie group has a characteristic almost connected locally compact subgroup which is a product of a finite number of copies of the reals and a compact abelian group such that the factor group modulo this characteristic subgroup is a compactly generated prodiscrete group without nontrivial compact subgroups.Mathematics Subject Classification (1991): 22B, 22E 相似文献
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群类理论是在有限可解群研究工作的基础上发展起来的,但近年来对有限群论的许多方面都起到越来越大的作用.在考察群类性质时,注意到一个Fitting类(?)在可解群G中的(?)内射子具有Sylow子群所具有的某些性质,并且关于Sylow定理中(Sy13),证明了对于群的本原子群,成立更强的结论. 相似文献
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YEN-SHENG CHIANG 《The Journal of mathematical sociology》2013,37(1):47-69
We present a simple combinatorial model of group decision‐making in a dichotomous choice situation. The independent variables in the model are group size and mean judgmental competence of group members. The dependent variables are the probabilities that the majority judgment of the group will be correct and that the best member of the group will be more likely to be correct than the group majority. Two applications of this model are given: one a determination of isocompetence curves of groups of differing sizes and mean competence levels, the other an explication of the potential mechanisms accounting for Parkinson's only partly tongue‐in‐cheek observation that the point of ineffectiveness in a group seems to be reached when its total membership exceeds 20 or 21. 相似文献
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V. K. Beloshapka 《Mathematical Notes》2007,82(3-4):461-463
Local polynomial models of real submanifolds of complex spaces were constructed and studied in a series of papers. Among the main features of model surfaces, there is the property that the dimension of the local group of holomorphic symmetries of a germ does not exceed that of the same group of the tangent model surface of this germ. In the paper, this assertion is rendered much stronger; namely, it is proved that the connected component of the identity element in the symmetry group of a nondegenerate germ is isomorphic as a Lie group to a subgroup of the symmetry group of its tangent model surface. 相似文献