共查询到20条相似文献,搜索用时 62 毫秒
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设N,H是任意的群.若存在群G,它具有正规子群≤Z(G),使得≌N且G/≌H,则称群G为N被H的中心扩张.本文完全分类了当N为p~3阶初等交换p群及H为内交换p群时,N被H的中心扩张得到的所有不同构的群.从而我们完全分类了初等交换p群被内交换p群的中心扩张得到的所有不同构的群. 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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称有限群G为QCC群,若对G中的任意非交换商群G/N,均有Z(G/N)循环,其中1≠N(?)G.本文对QCCp群进行了研究,证明了非交换QCCp群或为特殊群、或换位子群的阶为p、或生成元的个数为2.进一步,证明了二元生成且|G|≠35的非交换QCC 2群(QCC 3群)G为内交换群或极大类群. 相似文献
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设N,H是任意的群.若存在群G,它具有正规子群N≤Z(G),使得N≌N且G/N≌H,则称群G为N被H的中心扩张.本文完全分类了当N为循环p群,H为内交换p群时,N被H的中心扩张得到的所有不同构的群. 相似文献
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研究了阶为p(m(m+1)/2)且交换子群的最大阶为p(m)的有限群,得到了这类特殊的p群的几个性质,给出了满足极大类条件的这类p群的同构分类. 相似文献
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群环理论将群论和环论有机地结合了起来,是代数学中的重要分支之一,其中增广理想和增广商群是群环理论中的一个经典课题.设G有限群,分别记的Burnside环及其增广理想为Ω(G)和Δ(G).本文对任意正整数n,具体构造了Δ~n(I_p)作为自由交换群的一组基,并确定了商群Δ~n(I_p)/Δ~(n+1)(I_p)的结构,其中I_p=〈a,b|a~(p~2)=b~p=1,b~(-1)ab=a~(p+1)〉,p为奇素数. 相似文献
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James P. Cossey 《代数通讯》2018,46(8):3356-3364
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Antonio Tortora 《代数通讯》2013,41(2):431-438
For any integer n ≠ 0,1, a group G is said to be “n-Bell” if it satisfies the identity [x n ,y] = [x,y n ]. It is known that if G is an n-Bell group, then the factor group G/Z 2(G) has finite exponent dividing 12n 5(n ? 1)5. In this article we show that this bound can be improved. Moreover, we prove that every n-Bell group is n-nilpotent; consequently, using results of Baer on finite n-nilpotent groups, we give the structure of locally finite n-Bell groups. Finally, we are concerned with locally graded n-Bell groups for special values of n. 相似文献
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Bijan Taeri 《代数通讯》2013,41(3):894-922
Let n be an integer greater than 1. A group G is said to be “ n-rewritable” whenever for every n elements x 1,…,x n of G, there exist distinct permutations τ, σ on the set {1,2,…, n} such that x τ(1) ··· x τ(n) = x σ (1) ··· x σ (n). In this article, we complete the classification of 3-rewritable finite nilpotent groups and prove that a finite nilpotent group G is 3-rewritable if and only if G has an abelian subgroup of index 2 or the derived subgroup has order < 6. 相似文献
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I. Lizasoain 《数学学报(英文版)》2010,26(3):405-418
Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups (G-groups). In this paper we establish a decomposition theorem for irreducible G-groups which expresses a suitable irreducible G-group as a tensor product of two projective G-groups in a similar way to the celebrated theorem of Clifford for linear representations. Moreover, we study the non-abelian minimal normal subgroups of G in which this decomposition is possible. 相似文献
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In 1960, Baumslag, following up on work of Cernikov for the 1940s, proved that a hypercentral p-group G with G = G p is a divisible Abelian group. In this article, we provide an interesting generalization of this 45 year old result: If a hypercentral p-group G satisfies |G:G p |<∞ (of course, it contains G = G p ), there exists a normal divisible Abelian subgroup D such that |G:D|<∞. 相似文献
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A. Jaikin-Zapirain 《Mathematische Zeitschrift》2006,253(2):333-345
In this paper we prove that if R is a commutative Noetherian local pro-p domain of characteristic 0, then every finitely generated R-standard group is linear.
This work has been partially supported by the FEDER, the MEC Grant MTM2004-04665 and the Ramón y Cajal Program. 相似文献
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《代数通讯》2013,41(5):1417-1425
ABSTRACT Let n be an integer greater than 1. A group G is said to be n-rewritable (or a Qn-group) if for every n elements x1, x2,…,xn in G there exist distinct permutations σ and τ in Sn such that xσ(1)xσ (2) ??? xσ(n) = xτ(1)xτ(2) ??? xτ(n). In this paper, we characterize all 3-rewritable nilpotent 2-groups of class 2. Also we have found a bound for the nilpotency class of certain nilpotent 3-rewritable groups, and have shown that 3-rewritable groups satisfy a certain law. 相似文献
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A Garside group is a group admitting a finite lattice generating set
. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π, 1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice
, and there is a simple sufficient condition that implies G is a duality group. The universal covers of these K(π, 1)s enjoy Bestvina's weak nonpositive curvature condition. Under a certain tameness condition, this implies that every
solvable subgroup of G is virtually Abelian. 相似文献
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王登银 《数学物理学报(B辑英文版)》2007,27(2):317-328
All parabolic subgroups and Borel subgroups of PΩ(2m 1, F) over a linear-able field F of characteristic 0 are shown to be complete groups, provided m > 3. 相似文献