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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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该文给出了三个以p群为自同构群的p6阶群,并得到了它们的自同构群的阶.在这里p表示奇素数. 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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利用外FC-群的结果,给出了其真商群为周期FC-群但它本身不具备这种性质的群的结构的满意描述. 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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该文给出了三个以 p 群为自同构群的 p6 阶群, 并得到了它们的自同构群的阶. 在这里 p 表示奇素数. 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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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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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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In the paper, necessary and sufficient conditions for an Abelian group A to be isomorphic to the endomorphism group End(A) are obtained. The classes of periodic Abelian groups, divisible Abelian groups, nonreduced Abelian groups, and reduced algebraically compact Abelian groups are considered. For certain classes of Abelian groups, the isomorphism problem for a group and its endomorphism group is solved under the assumption that the endomorphism group itself has the corresponding property. 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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本文研究了泛欧氏空间的Clifford群、扭群、旋群,它们为Clifford代数中选出极好的一类子群.利用Clifford代数理论方法,获得了泛欧氏空间中Clifford群、扭群、旋群及其李代数的结构及它们之间的关系,并且得到了它们的李代数. 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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《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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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