共查询到20条相似文献,搜索用时 296 毫秒
1.
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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阎满富 《纯粹数学与应用数学》1999,15(4):88-91
一个有限p群p称为亚循环的,如果P有一个循环的正规子群A,使得PA是循环的.1973年King在文[2]中对亚循环p群进行了分类;在文[4,5]中M.F.NewmanandMingYaoXu发现了这些群的新的表示,给出了新的分类方法,这种方法是由p群生成算法(见文[3])得到的.本文的目的是给这些结果的另一种证明,与p群生成算法是不相关的. 相似文献
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依据模糊子群与子群列之间的关系,通过分析具有极大循环子群的P-群的子群列的构造特点,给出了能够反映具有极大循环子群的P-群的模糊子群构造特征的模糊子群的阶、极大模糊子群和模糊子群的等价类数的计算公式. 相似文献
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《数学的实践与认识》2020,(2)
设N,H是任意的群.若存在群G,它具有正规子群■,使得■且■,则称群G为N被H的中心扩张.完全给出了当|N|=p,H为奇阶亚循环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
11.
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
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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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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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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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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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O. Surmanidze 《Journal of Mathematical Sciences》2014,197(6):807-857
In this paper, we study linearly topological groups. We introduce the notion of a weakly linearly compact group, which generalizes the notion of a weakly separable group, and examine the main properties of such groups. For weakly linearly compact groups, we construct the character theory and present an algebraic characterization of some classes of such groups. Some well-known theorems for periodic Abelian groups are generalized for the case of linearly discrete, topological Abelian groups; for linearly compact and linearly discrete topological Abelian groups, we also construct the character theory and study some important properties of linearly discrete groups. For linearly discrete, topological Abelian groups, we analyze the splittability condition (Theorem 3.12) and present the characteristic condition of decomposability of a discrete group G into the direct sum of rank-1 groups. We also present an algebraic characterization of linearly compact groups. We introduce the notion of a weakly linearly compact, topological Abelian group, which generalizes the notion of a weakly separable Abelian group, and examine some properties of such groups. These groups are a generalization of fibrous Abelian groups introduced by Vilenkin. We give an algebraic characterization of divisible, weakly locally compact Abelian groups that do not contain nonzero elements of finite order (Proposition 7.9). For weakly locally compact Abelian groups, we construct universal groups. 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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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