共查询到19条相似文献,搜索用时 140 毫秒
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本文在研究一个生成元的Abel群的基础上,建立了两个生成元的Abel群到实数加群的同态方法,并对自由Abel群上的超群结构进行了分析与研究,给出了正规超群的分类,进而推进一个重要结论:自由Abel群构于实数加群及其子群. 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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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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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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本决定了D1和E6型Weyl群扭子群的所有扩群,这为确定相应Chevalley群扭子群的所有扩群奠定了基础。 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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在本文中,我们讨论了带作用群的群系的临界结构,给出了处理允许某些作用群的群的问题的一般方法,作为应用,我们特别给出了关于幂零群及p-幂零群的一些结果。 相似文献
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As an outgrowth of the study of algebraic geometry over groups, discriminating groups were introduced. Many important universal type groups such as Higman's universal group and Thompson's group F were shown to be discriminating. Squarelike groups were then introduced to better capture axiomatic properties of discrimination. In the present article squarelike groups are reinterpreted in terms of discrimination of quasi varieties, and the relationship with an older version of discrimination, termed varietal discrimination here, is studied. 相似文献
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本文第一部分对组台群论的发展史作了一个简要的回顾.然后重点介绍近20年来组合群论领域中的三个热点课题:即双曲群,自动机群和群的Dehn函数的有关概念,并对相关的重要研究成果给予概述,其中包括作者本人在群的二阶Dehn函数的研究工作中的若干成果.最后提出9个公开问题。 相似文献
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Dikran N. Dikranjan 《代数通讯》2013,41(15):6073-6090
We study classes of abelian groups related to sequential com¬pactness and its generalizations (completeness, coarseness and sequential pre-compactness) in convergence groups. In particular, we describe the algebraic structure of the abelian groups on which every coarse convergence is complete and we prove that: i) every abelian group admits a sequentially precompact convergence; ii) every algebraically compact abelian group admits a sequen¬tially compact convergence. 相似文献
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I. Kh. Bekker 《Mathematical Notes》1997,61(4):399-408
In the paper, sufficient conditions for the splittability of mixed Abelian groups with periodic automorphism groups are established.
Classes of mixed splittable Abelian groups with perfect holomorphs are distinguished.
Translated fromMaternaticheskie Zametki, Vol. 61, No. 4, pp. 483–493, April, 1997.
Translated by A. I. Shtern 相似文献
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V. I. Senashov 《Mathematical Notes》1997,62(4):480-487
The class of generalized Chernikov groups is characterized, i.e., the class of periodic locally solvable groups with the primary
ascending chain condition. The name of the class is related to the fact that the structure of such groups is close to that
of Chernikov groups. Namely, a Chernikov group is defined as a finite extension of a direct product of finitely many quasi-cyclic
groups, and a generalized Chernikov group is a layer-finite extension of a direct productA of quasi-cyclicp-groups with finitely many factors for each primep such that each of its elements does not commute elementwise with only finitely many Sylow subgroups ofA. A theorem that characterizes the generalized Chernikov groups in the class of groups with involution is proved.
Translated fromMatematicheskie Zametki, Vol. 62, No 4, pp. 577–587, October, 1997.
Translated by A. I. Shtern 相似文献
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A. N. Starkov 《Mathematical Notes》1998,63(2):233-241
A criterion for a wide class of topological groups which includes linear discrete groups and Lie groups to be Tychonoff groups
is established. The main result provides a criterion for an almost polycyclic group to have the Tychonoff property. By the
well-known Tits alternative, this yields the required criterion for linear discrete groups. In conclusion it is pointed out
that a particular case of the presented proof yields a Tychonoff property criterion for Lie groups. In addition, an example
of a polycyclic group without Tychonoff subgroups of finite index is constructed.
Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 269–279, February, 1998.
The author wishes to express his gratitude to R. I. Grigorchuk for setting the problem and his interest in the work.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00182 and by the American Mathematical
Society Fund. 相似文献
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《Journal of Pure and Applied Algebra》2022,226(5):106931
The purpose of this paper is to show the vastness of the class of generalized strongly monomial groups and the implication of its study on monomiality questions studied by group theorists. The so called generalized strongly monomial groups, which is a generalization of strongly monomial groups introduced by Olivieri, del Río and Simón, arose in a recent work of authors while understanding the algebraic structure of rational group algebras. 相似文献
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研究内p-闭群的结构是一个很活跃的课题.对于p=2,3,5的内p-闭群的结构已经被确定(见[1,2,3]).本文确定内7-闭单群的结构 相似文献