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设A是秩为n(n≥2)的自由Abel群,α是利用A直和分量上的循环置换与数乘构造的一个A的自同构.作A与α的半直积G=A×〈α〉,本文给出了这类多重循环群G的同构分类,以及它构成超可解群和幂零群的充要条件. 相似文献
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一类无限的多重循环群 总被引:2,自引:0,他引:2
刘合国 《数学年刊A辑(中文版)》1995,(3)
设G是无限的多重循环群,如果对G的每个有限商群G,G的所有Abel子群都是3元生成的,那么G ̄(7)=1且G是4元生成的. 相似文献
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刘合国 《数学年刊A辑(中文版)》2000,(6)
设G是个有限生成的超Abel群,若G满足下列的条件之一: (i) G的 2一生成的子群都是多重循环群; (ii)G/Z*(G)是多重循环群,Z*(G)表示G的超中心(Hypercentre); (iii) G/△十(G)是多重循环群, △+(G)表示 G的所有有限正规子群生成的子群,则G是个多重循环群. 相似文献
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设G是剩余有限minimax可解群,α是G的自同构且φ:G→G(g→[g,α])是满射,则有以下结果:(1)当α~p=1时,G是幂零类不超过h(p)的幂零群的有限扩张,其中h(p)是只与p有关的函数;(2)当α~4=1时,G存在一个指数有限的特征子群H,使得H″≤Z(H)和C_H(α~2)是Abel群.并且C_G(α~2)和G/[G,α~2]都是Abel群的有限扩张. 相似文献
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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
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We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group
is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated
Fuchsian group and of every free-by-finite group is residually finite. 相似文献
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设p为奇素数,本文将用一些新的技巧来证明,当P是阶小于P^11的交换P-群时,自同构群方程Aut(X)=P无解。这个结果使MachHale在1983年的工作得到了突破,并且我们所给的方法具有广泛性。 相似文献
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给出了带极大或极小条件的Abel群A的自同构群以及自同态环的相伴Lie环是可解或幂零的充要条件.同时也给出了群A=Q_(π1)⊕Q_(π2)⊕…⊕Q_(πr)的自同构群是可解或幂零的充要条件,以及群A的自同态环的相伴Lie环是可解或幂零的充要条件. 相似文献
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本文给出了多重循环群的Fiting子群的几条性质,所得结果深化了Malcev关于多重循环群的经典工作. 相似文献
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Raimundo Bastos 《代数通讯》2013,41(10):4177-4184
Let m, n be positive integers. Suppose that G is a residually finite group in which for every element x ∈ G there exists a positive integer q = q(x) ≤ m such that xq is left n-Engel. We show that G is locally virtually nilpotent. Further, let w be a multilinear commutator and G a residually finite group in which for every product of at most 896 w-values x there exists a positive integer q = q(x) dividing m such that xq is left n-Engel. Then w(G) is locally virtually nilpotent. 相似文献
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For a group G, an HNN-extension of polycyclic groups, we give two necessary and sufficient conditions for G to be hopfian. One is based on the nature of the endomorphism of G and the other on the nature of the associated subgroups of G. At the end, we give an application for HNN-extensions of nilpotent groups. 相似文献
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Aaron Clark 《代数通讯》2013,41(5):1615-1623
In this article which is partly a continuation of Goldstein (1999), we give some necessary and sufficient conditions for an element of a free group to be primitive. For certain words x, we also give a lower bound on the length of words obtained from x by an automorphism. In the last section we give another proof of the Primitivity Theorem recently proven by Lee, using ideas from the first part of the article. 相似文献
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Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G→ G defined by g~φ= [g, α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning the condition on surjectivity, we prove that C_G(α~2) and G/[G, α~2] are both abelian-by-finite. 相似文献