共查询到19条相似文献,搜索用时 406 毫秒
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本文利用外FA-群(JNFA-groups)的结果,给出了其真商群为满足极小条件的FO-群但它本身不具备这种性质的群的结构的满意的描述。 相似文献
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如果有限群G的每个子群与G的某个商群同构,则称群G为s-自对偶群.如果s-自对偶群G的每个商群与G的某个子群同构,则称群G为自对偶群.本文分类了每个真商群均为s-自对偶群的有限p-群.作为推论,本文还分类了每个真截段均为s-自对偶群的有限p-群,每个真商群均为自对偶群的有限p-群,以及每个真截段均为自对偶群的有限p-群... 相似文献
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阶为某素数p的方幂的自同构如果不是内自同构,则称其为外p-自同构.如果φ是群G的外p-自同构且o(φ)=p,其中φ是φ在Out(G)=Aut(G)/Inn(G)中的自然同态像,则称φ为群G的拟极小外p-自同构.设φ是有限p-群G的任意拟极小外p-自同构,给出了|C_G(φ)|≤p时G的结构. 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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称有限p群G为ACT群,如果对每个交换子群H,其正规核HG=1或HG=H.又称p群G是CC群,如果对每个非正规交换子群H,有HG=1或HG在G中的指数为p.本文分类了ACT群和CC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: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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本文首先将Hal定理推广为:设N为G的正规子群,若N为Enπ群,G/N为Dπ群,则G为Dπ群.在此基础上得到了群G为Enπ群的充要条件为:(1)G存在正规子群N,满足N及G/N为Enπ群;(2)对任意p∈π,任意q∈π {p}及任意p 元素x,CG(x)含G的Sylowq 子群.另外,我们对非Able单群的情形也进行了一些讨论. 相似文献
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In this paper,the automorphism group of G is determined,where G is a 4 × 4 upper unitriangular matrix group over Z.Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G,G /ζG and ζG,then (i) InnG ■ K ■ AutG;(ii) AutG/K≌=G1×D8×Z2,where G1=(a,b,c|a4=b2=c2=1,ab=a-1,[a,c]= [b,c]=1 ;(iii) K/Inn G≌=Z×Z×Z. 相似文献
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对于有限群G的每一主因子H/K来说,若G的子群L满足LH=LK或者L∩H=L∩K,则称L是G的CAP-子群.本文通过假设G的每个非循环Sylow子群P有一个子群D使得1〈|D|〈|P|,且P的所有阶为|D|和2|D|(若P是非交换2-群且|P∶D|〉2)的子群H是G的CAP-子群,得到G为p-幂零群的一个结果. 相似文献
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A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure of a group under the assumption that every subgroup with order pm of a Sylow p-subgroup P of G is SS-quasinormal in G for a fixed positive integer m. Some interesting results related to the p-nilpotency and supersolvability of a finite group are obtained. For example, we prove that G is p-nilpo... 相似文献
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群G的子群H称为G的CAP-嵌入子群,如果对于|H|的每个素因子p,存在G的某个CAP-子群K,使得H的某个Sylow p-子群也是K的一个Sylowp-子群.本文通过假定G的p-Fitting子群F_p(G)的某个Sylow p-子群的每个极大子群是G的CAP-嵌入子群,得到一些新的结果. 相似文献
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Jeremy Haefner 《代数通讯》2013,41(8):2765-2782
The following two results are proven. (i) Let G be a finitely generated torsion-free linear group. If every torsion-free section of G is an R-group, then G is soluble of finite rank. Conversely, if G has finite rank, then it has a subgroup of finite index, in which every torsion-free section is an R-group. Let G be a finitely generated torsion-free soluble group. If in every torsion-free section of G the normalizer of each isolated subgroup is isolated, then G has finite rank. Conversely, if G has finite rank, then it has a subgroup K of finite index such that in every torsion-free section of K the normalizer of each isolated subgroup is isolated. 相似文献
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CHEN GuiYun & LI JinBao School of Mathematics Statistics Southwest University Chongqing China School of Mathematical Sciences Xuzhou Normal University Xuzhou China 《中国科学A辑(英文版)》2009,(2)
Let A be a subgroup of a group G and X be a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we investigate further the influence of X-semipermutability of some subgroups on the structure of finite groups. Some new criteria for a group G to be supersoluble or p-nilpotent are obtained. 相似文献
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Houshang Behravesh Mohammad Hossein Jafari 《数学物理学报(B辑英文版)》2007,27(2):297-300
The quantities c(G), q(G) and p(G) for finite groups were defined by H. Behravesh. In this article, these quantities for the alternating group An and the symmetric group Sn are calculated. It is shown that c(G) = q(G)=p(G) = n, when G = An or Sn. 相似文献