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李志秀 《数学的实践与认识》2016,(14):294-296
研究了内交换p-群G是capable群需要满足的条件,得到了这类群是capable群的充要条件.并由内交换p-群G构造得到了群H,使得H满足HH/Z(H)≌G. 相似文献
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本文给出了离散群的可数内不变平均的具体的表达式.证明了由可数内不变平均生成的向量空间的维数等于极小内不变平均的基数,并得到了内顺从群的一些新的刻划. 相似文献
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内-FI群和外-FI群 总被引:1,自引:0,他引:1
若群G的同构子群类均是有限的,则称群G为FI群,本文分别研究了所谓的内-FI群和外-FI群的性质,给出了这两类无限群的令人满意的结构描述。 相似文献
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研究某些子群同构的有限p-群是很有趣的.例如,Hermann和Mann都曾研究过极大子群都同构的有限p-群,但这类群的结构非常复杂,到现在人们都没能给出其分类.研究了特定阶的子群都同构且交换的有限p-群,并给出其分类. 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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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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设G是一个有限p-群.若G的真子群的导群的阶都整除pi,则称G为Di-群.我们给出了所有D1-群的一个刻画.这回答了Berkovich提出的一个问题. 相似文献
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Let f be a permutation of V(G). Define δf(x,y)=|dG(x,y)-dG(f(x),f(y))| and δf(G)=∑δf(x,y) over all the unordered pairs {x,y} of distinct vertices of G. Let π(G) denote the smallest positive value of δf(G) among all the permutations f of V(G). The permutation f with δf(G)=π(G) is called a near automorphism of G. In this paper, we study the near automorphisms of cycles Cn and we prove that π(Cn)=4⌊n/2⌋-4, moreover, we obtain the set of near automorphisms of Cn. 相似文献
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设$H$是有限群$G$的一个子群,若对任意$g\in G$, $H\cap H^g=1$或者$H$,则称$H$为TI-子群. 设$G$是一个所有二极大子群为TI-子群的有限群,本文证明了$G$的每个类保持Coleman自同构是内自同构. 作为本结果的一个直接推论,得到了这样的群$G$有正规化子性质. 相似文献
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设$G$是一个本原群,证明了存在某个素数$p$使得$G$的每个$p$-中心自同构是内自同构. 作为应用,证明了$G$的全形的每个Coleman自同构均为内自同构. 特别地,正规化子性质对对所讨论的这些群都成立. 另外也得到了其他一些相关结果. 相似文献
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Zahedeh Azhdari 《代数通讯》2013,41(10):4133-4139
Let G be a group and Autc(G) be the group of all central automorphisms of G. We know that in a finite p-group G, Autc(G) = Inn(G) if and only if Z(G) = G′ and Z(G) is cyclic. But we shown that we cannot extend this result for infinite groups. In fact, there exist finitely generated nilpotent groups of class 2 in which G′ =Z(G) is infinite cyclic and Inn(G) < C* = Autc(G). In this article, we characterize all finitely generated groups G for which the equality Autc(G) = Inn(G) holds. 相似文献
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严荣沐 《数学物理学报(A辑)》2006,(Z1)
In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reirihardt domains. and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimension n2 - 2 (where n is the dimension of domain). 相似文献
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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
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本文研究了三角代数的自同构.利用三角代数的基本概念及自同构定义,得到三角代数的自同构形式,并刻画了其内自同构的具体形式. 相似文献
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Manoj K. Yadav 《代数通讯》2013,41(12):4576-4592
We obtain certain results on a finite p-group whose central automorphisms are all class preserving. In particular, we prove that if G is a finite p-group whose central automorphisms are all class preserving, then d(G) is even, where d(G) denotes the number of elements in any minimal generating set for G. As an application of these results, we obtain some results regarding finite p-groups whose automorphisms are all class preserving. 相似文献
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Let be an almost crystallographic (AC-) group, corresponding to the simply connected, connected, nilpotent Lie group and with holonomy group . If , there is a faithful representation . In case is crystallographic, this condition is known to be equivalent to or . We will show (Example 2.2) that, for AC-groups , this is no longer valid and should be adapted. A generalised equivalent algebraic (and easier to verify) condition is presented (Theorem 2.3). Corresponding to an AC-group and by factoring out subsequent centers we construct a series of AC-groups, which becomes constant after a finite number of terms. Under suitable conditions, this opens a way to represent faithfully in (Theorem 4.1). We show how this can be used to calculate . This is of importance, especially, when is almost Bieberbach and, hence, is known to have an interesting geometric meaning.