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1.
自同构群是循环群被交换群扩张的有限群 总被引:1,自引:0,他引:1
设C是有限群,AutG=AB,,A是交换群且每Sylow子群的秩≤2,B是循环群,本文得出了G的结构,特别地,证明了AutG是秩≤2的交换群时,G循环。 相似文献
2.
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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设G是个有限可解解,若对G的每个商群H,H的正规Abel子群都是可以由2元生成的,则称G为AD2-群,在本文里,我们证明了:如果G是个AD2-群,那么G是3元生定的,且G^(6)=1。另外,我们举了2个例子,说明这些界都是最好的。 相似文献
5.
本文证明了有限群G是Abel群当且仅当G_r满足下列条件:(Ⅰ) G有一个幂自同构 a使得 CG(a)是一个初等 AbelZ一群.(Ⅱ)G没有子群与2-群<a,b|a~2~n=b~2~m=1,a~b=a~(1+2)~(n-1)>同构,其中n≥3,n≥m.利用该结果,作者还证明若有限群G有一个幂自同构a使得C_G(a)是一个初等Abel2-群,则G是幂零群 相似文献
6.
一类不能作为自同构群的奇阶群 总被引:2,自引:0,他引:2
本文考虑如下问题:怎样的有限群可以作为另一个有限群的全自同构群?我们首先证明,若有限群K有一个正规Sylowp-子群使得|K:Z(K)|p=p2,那么K有2阶自同构.利用这个结果,我们证明了,若奇阶群G具有阶Psm(1≤s≤3),p为|G|的最小素因子,pm,m无立方因子,则G不可能作为全自同构群. 相似文献
7.
构造出D2m型Chevalley群扩群G,证明了其唯一性,并讨论了文「1」中构造的An型G的唯一性。 相似文献
8.
如果对多重循环群G的每个有限剩余G,G的真子群都具有可以由二元生成的,那么我们就把G叫做RD2-群,在本文里,我们确定了无限的RD2-群的结构,证明了RD2-群是可以由二元生成的,这些结构推广了作者已经得到了关于无限的可解SD2群的全部结果,见(4)。 相似文献
9.
非幂零极大子群指数为素数幂的有限群 总被引:7,自引:0,他引:7
郭秀云 《数学年刊A辑(中文版)》1994,(6)
本文证明了如下结果,1.设p是一个素数,如果有限群G的每一非幂零的极大子群的指数都为p的方幂,则G为可解群.2.如果有限群G的每一非幂零的极大子群的指数为素数幂,则G/S(G)1或PSL(2,7),其中S(G)表示G的最大可解正规子群. 相似文献
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11.
In the paper, on the basis of the notion of saturation introduced in [1], we give a characterization of locally finite simple groups
with an Abelian Sylow 2-subgroup in the classes of mixed and periodic groups. A part of the main results was announced in [2]. Theorem 2 of the paper generalizes results of [3, 4]. 相似文献
12.
Yu Chunhai 《模糊系统与数学》1993,(2)
In paper [1], it gave the concept and basic properties of L-fuzzy topological groups. This paper will enter the concept of quotient groups of L-fuzzy topological groups and will prove some properties of subgroups and quotient groups. The persent work is the continuation of [1] and hence all the conventions in [1] still hold good in the present paper. 相似文献
13.
Jan Jakubik 《Czechoslovak Mathematical Journal》2001,51(1):127-138
The notion of the half linearly ordered group (and, more generally, of the half lattice ordered group) was introduced by Giraudet and Lucas [2]. In the present paper we define the lexicographic product of half linearly ordered groups. This definition includes as a particular case the lexicographic product of linearly ordered groups. We investigate the problem of the existence of isomorphic refinements of two lexicographic product decompositions of a half linearly ordered group. The analogous problem for linearly ordered groups was dealt with by Maltsev [5]; his result was generalized by Fuchs [1] and the author [3]. The isomorphic refinements of small direct product decompositions of half lattice ordered groups were studied in [4]. 相似文献
14.
在《数学学报》2013年第56卷第4期中,"Suzuki-Ree群的自同构群的一个新刻画"一文证明了Aut(~2F_4(q)),q=2~f和Aut(~2G_2(q)),q=3~f,可由其阶分量刻画,其中f=3~s,s为正整数.本文证明了Aut(~2B_2(q)),q=2~f和Aut(2G2(q)),q=3~f,也可由其阶分量刻画,其中f为奇素数.结合二者得到结论:Suzuki-Ree单群的所有的素图不连通的自同构群皆可由其阶分量刻画. 相似文献
15.
Marian Deaconescu 《代数通讯》2013,41(1):215-219
This article classifies the groups X whose autocommutator subgroup [X, Aut(X)] is isomorphic to ? and the finite groups X for which [X, Aut(X)] ? C p has a prime number p of elements. 相似文献
16.
We give a necessary and sufficient condition for two Hopf algebras presented as central extensions to be isomorphic, in a
suitable setting. We then study the question of isomorphism between the Hopf algebras constructed in [AG] as quantum subgroups
of quantum groups at roots of 1. Finally, we apply the first general result to show the existence of infinitely many non-isomorphic
Hopf algebras of the same dimension, presented as extensions of finite quantum groups by finite groups.
Partially supported by CONICET, ANPCyT, Secyt (UNC) and Ministerio de Ciencia y Tecnología de la Provincia de Córdoba. 相似文献
17.
Victor Gerasimov 《Geometric And Functional Analysis》2009,19(1):137-169
Let a discrete group G act by homeomorphisms of a compactum in a way that the action is properly discontinuous on triples and cocompact on pairs.
We prove that such an action is geometrically finite. The converse statement was proved by P. Tukia [T3]. So, we have another
topological characterisation of geometrically finite convergence groups and, by the result of A. Yaman [Y2], of relatively
hyperbolic groups. Further, if G is finitely generated then the parabolic subgroups are finitely generated and undistorted. This answer to a question of B.
Bowditch and eliminates restrictions in some known theorems about relatively hyperbolic groups.
Received: April 2007, Revision: May 2008, Accepted: August 2008 相似文献
18.
Zhang Qinhai 《数学季刊》1996,(1)
Finite Groups with only S-seminormal or Selfnormal SubgroupsFiniteGroupswithonlyS-seminormalorSelfnormalSubgroups¥ZhangQinhai... 相似文献
19.
Dr. Rolf Struve 《Results in Mathematics》2005,48(1-2):168-183
A. Cayley [5] and F. Klein [12] were the first mathematicians who introduced the notion of a metric in a real projective space, by specializing a set of quadrics (called the absolute). We show in this paper, that from an algebraic point of view these projective spaces can be described by vector spaces, in which a metric structure is given by one or more symmetric bilinear forms. We study these Cayley- Klein vector spaces and their groups of automorphisms (orthogonal Cayley- Klein groups) over arbitrary commutative fields of characteristic ≠ 2. 相似文献