共查询到20条相似文献,搜索用时 78 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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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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本文根据有限Abel群G的自同构群A(G)的阶研究了群G的构造.利用有限交换群的一些性质,经过详细的理论推导,获得了|A(G)|=26p2(p为奇素数)的有限Abel群G的全部类型. 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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李志秀 《数学的实践与认识》2014,(22)
给定了一个群G,若存在另外的一个群H,能够使得H/Z(H)≌G,则称G是capable群.对cable群进行研究在p-群分类问题的研究中起着相当重要的作用.完全决定了亚循环的capable p-群G. 相似文献
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Javier Ribón 《Israel Journal of Mathematics》2018,227(1):289-329
We are interested in classifying groups of local biholomorphisms (or even formal diffeomorphisms) that can be endowed with a canonical structure of algebraic groups and their subgroups. Such groups are called finitedimensional. We obtain that cyclic groups, virtually polycyclic groups, finitely generated virtually nilpotent groups and connected Lie groups of local biholomorphisms are finite-dimensional. We provide several methods to identify finite-dimensional groups and build examples.As a consequence we generalize results of Arnold, Seigal–Yakovenko and Binyamini on uniform estimates of local intersection multiplicities to bigger classes of groups, including for example virtually polycyclic groups and in particular finitely generated virtually nilpotent groups. 相似文献
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S. V. Ludkovsky 《Journal of Mathematical Sciences》2007,147(3):6703-6846
Diffeomorphism groups and loop groups of manifolds on Banach spaces over non-Archimedean fields are defined. Moreover, for
these groups, finite-and infinite-dimensional manifolds over the corresponding fields are considered. The group structure,
the differential-geometric structure, and also the topological structure of diffeomorphism groups and loops groups are studied.
We prove that these groups do not locally satisfy the Campbell-Hausdorff formula. The principal distinctions in the structure
for the Archimedean and classical cases are found. The quasi-invariant measures on these groups with respect to dense subgroups
are constructed. Stochastic processes on topological transformation groups of manifolds and, in particular, on diffeomorphism
groups and on loop groups and also the corresponding transition probabilities are constructed. Regular, strongly continuous,
unitary representations of dense subgroups of topological transformation groups of manifolds, in particular, those of diffeomorphism
groups and loop groups associated with quasi-invariant measures on groups and also on the corresponding configurational spaces
are constructed. The conditions imposed on the measure and groups under which these unitary representations are irreducible
are found. The induced representations of topological groups are studied by using quasi-invariant measures on topological
groups.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 39, Functional
Analysis, 2006. 相似文献
13.
Tree-graded spaces are generalizations of R-trees. They appear as asymptotic cones of groups (when the cones have cut-points). Since many questions about endomorphisms and automorphisms of groups, solving equations over groups, studying embeddings of a group into another group, etc. lead to actions of groups on the asymptotic cones, it is natural to consider actions of groups on tree-graded spaces. We develop a theory of such actions which generalizes the well-known theory of groups acting on R-trees. As applications of our theory, we describe, in particular, relatively hyperbolic groups with infinite groups of outer automorphisms, and co-Hopfian relatively hyperbolic groups. 相似文献
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Square groups are quadratic analogues of abelian groups. Many properties of abelian groups are shown to hold for square groups. In particular, there is a symmetric monoidal tensor product of square groups generalizing the classical tensor product. 相似文献
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S. V. Ludkovsky 《Journal of Mathematical Sciences》2008,150(4):2123-2223
Diffeomorphism groups and loop groups of manifolds on Banach spaces over non-Archimedean fields are defined. Moreover, for
these groups, finite-and infinite-dimensional manifolds over the corresponding fields are considered. The group structure,
the differential-geometric structure, and also the topological structure of diffeomorphism groups and loops groups are studied.
We prove that these groups do not locally satisfy the Campbell-Hausdorff formula. The principal distinctions in the structure
for the Archimedean and classical cases are found. The quasi-invariant measures on these groups with respect to dense subgroups
are constructed. Stochastic processes on topological transformation groups of manifolds and, in particular, on diffeomorphism
groups and on loop groups and also the corresponding transition probabilities are constructed. Regular, strongly continuous,
unitary representations of dense subgroups of topological transformation groups of manifolds, in particular, those of diffeomorphism
group and loop groups associated with quasi-invariant measures on groups and also on the corresponding configurational spaces
are constructed. The conditions imposed on the measure and groups under which these unitary representations are irreducible
are found. The induced representations of topological groups are studied by using quasi-invariant measures on topological
groups.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 18, Functional Analysis, 2006. 相似文献
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The notion of “near isomorphism” for torsion-free Abelian groups of finite rank is well known. In particular, this concept turned out to be of importance for classifying almost completely decomposable groups. We extend near isomorphism to classes of torsion-free Abelian groups of infinite rank which are unions of bcd–groups, this is to say unions of groups which are bounded essential extensions of completely decomposable groups. Moreover, we show that nearly isomorphic groups of this class also have nearly isomorphic endomorphism rings considered as Abelian groups. 相似文献
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The splitting obstruction groups depend functorially on the square of fundamental groups. In the paper the problem of splitting along a submanifold of codimension two under some restrictions on the square of fundamental groups is considered. New exact sequences and commutative diagrams containing Wall groups, splitting obstruction groups, and surgery obstruction groups for manifold pairs are obtained. Examples of computation of splitting obstruction groups and natural maps are considered. 相似文献
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Grossman first showed that outer automorphism groups of 1-relator groups given by orientable surface groups are residually finite, whence mapping class groups of orientable surfaces are residually finite. Allenby, Kim and Tang showed that outer automorphism groups of cyclically pinched 1-relator groups are residually finite, whence mapping class groups of orientable and non-orientable surfaces are residually finite. In this paper we show that outer automorphism groups of certain conjugacy separable 1-relator groups are residually finite. 相似文献
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Peter Eisele 《Journal of Theoretical Probability》1993,6(4):671-691
For a locally compact groupG a condition in terms of probability measures and conjugation is introduced, which implies that limits of shifted convolution powers are always translates of idempotent measures. Such groups are called Tortrat groups. The connection between Tortrat groups and shifted convolution powers is established by the method of tail idempotents. Some construction principles for Tortrat groups are given and applied to show that compact groups, abelian groups, and more generally SIN-groups, as well as MAP-groups and almost connected nilpotent groups are of this type. The class of Tortrat groups is compared with another class investigated by A. Tortrat. 相似文献