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1.
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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二次极大子群中2阶及4阶循环子群拟中心的有限群 总被引:1,自引:0,他引:1
本文讨论2阶及4阶循环子群对群结构的影响.证明二次极大子群中2阶及4阶循环子群拟中心的有限群G同构于下列群之一:(1)G为2-闭群;(2)G为2-幂零群;(3)G≌S,;(4)G=PQ.其中P为2^4阶广义四元数群,Q≌C3;(5)G≌A5或SL(2,5). 相似文献
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《数学的实践与认识》2013,(23)
设N,H是任意的群.若存在群G,它有正规子群N≤Z(G),使得N≌N且G/N√≌H,则称群G为N被H的中心扩张.完全分类了当N为2阶循环群及H为极大类2群时,N被H的中心扩张得到的所有互不同构的群. 相似文献
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无限循环群被有限生成Abel群的中心扩张 总被引:1,自引:0,他引:1
设G是无限循环群被有限生成Abel群的中心扩张,T是G的中心ζG的挠子群.如果T的阶与ζG/(G'⊕T)的挠子群的阶互素,那么群G可分解为G=S×F×T,其中S= 这里d_i都是正整数,满足d_1|d_2|…|d_r,F是秩为s的自由Abel群,T是有限Abel群,T=Z_(e_1)⊕Z_(e_2)⊕…⊕Z_e_t,e_11,满足e_1|e_2|…|e_t,并且(d_1,e_t)=1.进一步,(d_1,d_2,…,d_T;s;e_1,e_2,…,e_t)是群G的同构不变量,即若群H也是无限循环群被有限生成Abel群的中心扩张,T_H是ζH的挠子群.如果T_H的阶与ζH/(H'⊕T_H)的挠子群的阶互索,那么G同构于H的充要条件是它们有相同的不变量.显然,这个结果涵盖了有限生成Abel群的结构定理. 相似文献
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曹洪平 《数学年刊A辑(中文版)》2004,(6)
设G是有限群,πe(G)表示G中元素的阶的集合,h(πe(G))表示满足πe(H)=πe(G)条件的有限群H的同构类类数,本文证明了例外型Chevalley群G2(q)的h函数值为1或∞. 相似文献
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设G是有限群,πe(G)表示G中元素的阶的集合,h(πe(G))表示满足πe(H)=πe(G)条件的有限群H的同构类类数,本文证明了例外型Chevalley群G2(q)的h函数值为1或∞. 相似文献
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《数学的实践与认识》2020,(2)
设N,H是任意的群.若存在群G,它具有正规子群■,使得■且■,则称群G为N被H的中心扩张.完全给出了当|N|=p,H为奇阶亚循环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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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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设G为有限群,且满足M(G)=M(~2G_2(3~(2n+1))),则G必有正规子群同构于~2G_2(3~(2n+1))).特别地,若|G|=|~2G_2(3~(2n+1))|,则G≌G_2(3~(2n+1)). 相似文献
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We prove that the Tate cohomology groups ?n(G∕Φ(G),Z(Φ(G))) are non-trivial, whenever G is a finite p-group of class 3, or the pth term of the upper central series of G contains Z(Φ(G)). This confirms a conjecture of Schmid for these groups. 相似文献
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Let H be a subgroup of a group G. We say that H satisfies the power condition with respect to G, or H is a power subgroup of G, if there exists a non-negative integer m such that H = G m = 〈 g m |g ? G 〉. In this note, the following theorem is proved: Let G be a group and k the number of nonpower subgroups of G. Then (1) k = 0 if and only if G is a cyclic group (theorem of F. Szász); (2) 0 < k < ∞ if and only if G is a finite noncyclic group; (3) k = ∞ if and only if G is a infinte noncyclic group. Thus we get a new criterion for the finite noncyclic groups. 相似文献
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In this paper, we complete the classification of those finite 3-groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ?[G] satisfies the multiplicative Jordan decomposition (MJD). In the nonabelian case, we show that ?[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 33 = 27. 相似文献
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A subgroup H of a finite group G is called Hall normally embedded in G if H is a Hall subgroup of the normal closure H G . Groups which contain a Hall normally embedded subgroup of order d for every factor d of | G | are characterized. Such groups are supersolvable with a cyclic nilpotent residual of square-free order. 相似文献
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A square matrix over the complex field with non-negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful permutation representation of G is denoted by p(G). The minimal degree of a faithful representation of G by quasi-permutation matrices over the rational and the complex numbers are denoted by q(G) and c(G) respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G. In this paper p(G), q(G), c(G) and r(G) are calculated for the groups PSU (3, q2) and SU (3, q2).AMS Subject Classification (2000): 20C15 相似文献
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Coy L. May 《代数通讯》2013,41(10):4402-4413
Let G be a finite group. The symmetric genus σ(G) is the minimum genus of any Riemann surface on which G acts. We show that a non-cyclic p-group G has symmetric genus not congruent to 1(mod p 3) if and only if G is in one of 10 families of groups. The genus formula for each of these 10 families of groups is determined. A consequence of this classification is that almost all positive integers that are the genus of a p-group are congruent to 1(mod p 3). Finally, the integers that occur as the symmetric genus of a p-group with Frattini-class 2 have density zero in the positive integers. 相似文献
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We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the free groups π1(G′) with G′⊆G finite. 相似文献
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Cao H. P. Chen G. Grechkoseeva M. A. Mazurov V. D. Shi W. J. Vasil'ev A. V. 《Siberian Mathematical Journal》2004,45(6):1031-1035
The spectrum of a finite group is the set of its element orders. A finite group G is said to be recognizable by spectrum, if every finite group with the same spectrum as G is isomorphic to G. The purpose of the paper is to prove that for every natural m the finite simple Chevalley group F
4(2
m
) is recognizable by spectrum. 相似文献
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Guo-ping TANG School of Mathematical Sciences Graduate University of Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2007,50(9):1280-1288
Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order p~r,i.e.,a finite homocyclic abelian group.LetΔ~n (G) denote the n-th power of the augmentation idealΔ(G) of the integral group ring ZG.The paper gives an explicit structure of the consecutive quotient group Q_n(G)=Δ~n(G)/Δ~(n 1)(G) for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups. 相似文献
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《代数通讯》2013,41(7):3519-3527
Abstract Let G and A be finite groups such that (|G|, |A|) = 1. Let K be an algebraically closed field with Char K = 0. Denote by K α G the twisted group algebra of G over K with factor set α. In this paper we prove that if A acts homogeneously on K α G, then there exists an action of A on G, and there is a one-to-one correspondence between the set of A-invariant irreducible K α G-modules and the set of irreducible K α C G (A)-modules. 相似文献