Results 11 to 20 of about 51,537 (200)
Abelian subgroups of Garside groups [PDF]
Communications in Algebra, 2008 In this paper, we show that for every abelian subgroup $H$ of a Garside group, some conjugate $g^{-1}Hg$ consists of ultra summit elements and the centralizer of $H$ is a finite index subgroup of the normalizer of $H$.
Alonso J. M. +19 more
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Characterizing Subgroups of Compact Abelian Groups
Journal of Pure and Applied Algebra, 2004 We prove that every countable subgroup of a compact metrizable abelian group has a characterizing set. As an application, we answer several questions on maximally almost periodic (MAP) groups and give a characterization of the class of (necessarily MAP ...
Dikranjan, Dikran, Kunen, Kenneth
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Abelian Subgroups of Topological Groups [PDF]
Transactions of the American Mathematical Society, 1984 In [1] Šmidt’s conjecture on the existence of an infinite abelian subgroup in any infinite group is settled by counterexample. The well-known Hall-Kulatilaka Theorem asserts the existence of an infinite abelian subgroup in any infinite locally finite group. This paper discusses a topological analogue of the problem.
Grosser, Siegfried K. +1 more
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Solitary subgroups of Abelian groups
Expositiones Mathematicae, 2021 A subgroup \(K\) of an abelian group \(G\) is called solitary if \(G\) contains no other subgroup isomorphic to \(K\). The paper is dedicated to the study of solitary subgroups for some important classes of abelian groups. Complete descriptions are presented in Theorem 3 and Theorem 4.
Călugăreanu, Grigore +1 more
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Groups with Finitely Many Isomorphism Classes of Non-Normal Subgroups [PDF]
Advances in Group Theory and Applications, 2020 We study groups in which the non-normal subgroups fall into finitely many isomorphism classes. We prove that a locally generalized radical group with this property is abelian-by-finite and minimax.
Leonid A. Kurdachenko +2 more
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Isolated subgroups of finite abelian groups [PDF]
Czechoslovak Mathematical Journal, 2022 We say that a subgroup $H$ is isolated in a group $G$ if for every $x\in G$ we have either $x\in H$ or $\langle x\rangle\cap H=1$. In this short note, we describe the set of isolated subgroups of a finite abelian group. The technique used is based on an interesting connection between isolated subgroups and the function sum of element orders of a finite
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Planarity of Inclusion Graph of Cyclic Subgroups of Finite Group [PDF]
Mathematics Interdisciplinary Research, 2020 Let G be a finite group. The inclusion graph of cyclic subgroups of G, Ic(G), is the (undirected) graph with vertices of all cyclic subgroups of G, and two distinct cyclic subgroups ⟨a⟩ and ⟨b⟩, are adjacent if and only if ⟨a⟩ ⊂ ⟨b⟩ or ⟨b⟩ ⊂ ⟨a⟩. In this
Zahra Garibbolooki, Sayyed Heidar Jafari
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Balanced Subgroups of Abelian Groups [PDF]
Transactions of the American Mathematical Society, 1975 The balanced subgroups of Fuchs are generalised to arbitrary abelian groups. Projectives and injectives with respect to general balanced exact sequences are classified; a new class of groups is introduced in order to classify these projectives.
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n-capability of A-groups [PDF]
Mathematics Interdisciplinary Research, 2020 Following P. Hall a soluble group whose Sylow subgroups are all abelian is called A-group. The purpose of this article is to give a new and shorter proof for a criterion on the capability of A-groups of order p2q, where p and q are distinct primes ...
Marzieh Chakaneh +2 more
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On the Classification Problem for Rank 2 Torsion-Free Abelian Groups [PDF]
, 2000 We study here some foundational aspects of the classification problem for torsion-free abelian groups of finite rank. These are, up to isomorphism, the subgroups of the additive groups (Q^n, +), for some n = 1, 2, 3,....
Kechris, Alexander S.
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