Results 1 to 10 of about 52,191 (255)
On T-Characterized Subgroups of Compact Abelian Groups [PDF]
Axioms, 2015 A sequence \(\{ u_n \}_{n\in \omega}\) in abstract additively-written Abelian group \(G\) is called a \(T\)-sequence if there is a Hausdorff group topology on \(G\) relative to which \(\lim_n u_n =0\).
Saak Gabriyelyan
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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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Characterized Subgroups of Topological Abelian Groups [PDF]
Axioms, 2015 A subgroup H of a topological abelian group X is said to be characterized by a sequence v = (vn) of characters of X if H = {x ∈ X : vn(x) → 0 in T}. We study the basic properties of characterized subgroups in the general setting, extending results known ...
Dikran Dikranjan +2 more
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Subgroup transitivity in abelian groups [PDF]
Proceedings of the American Mathematical Society, 1998 The authors study notions of transitivity in abelian \(p\)-groups that are based on subgroups rather than elements. Recall that two subgroups of \(G\) are called equivalent if there is an automorphism of \(G\) that maps one to the other. Two equivalent subgroups \(H\) and \(H'\) of \(G\) are strongly equivalent if, for any isomorphism \(\varphi\colon G/
Paul Hill, Jane Kirchner West
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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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Factorizing profinite groups into two Abelian subgroups [PDF]
International Journal of Group Theory, 2013 We prove that the class of profinite groups $G$ that have a factorization $G=AB$with $A$ and $B$ abelian closed subgroups, is closed under taking strict projective limits.This is a generalization of a recent result by K.H.~Hofmann and F.G.~Russo.As an ...
Wolfgang Herfort
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On infinite anticommutative groups [PDF]
International Journal of Group Theory, 2023 We completely describe the structure of locally (soluble-by-finite) groups in which all abelian subgroups are locally cyclic. Moreover, we prove that Engel groups with the above property are locally nilpotent.
Costantino Delizia, Chiara Nicotera
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Torsion locally nilpotent groups with non-Dedekind norm of Abelian non-cyclic subgroups
Karpatsʹkì Matematičnì Publìkacìï, 2022 The authors study relations between the properties of torsion locally nilpotent groups and their norms of Abelian non-cyclic subgroups. The impact of the norm of Abelian non-cyclic subgroups on the properties of the group under the condition of norm non ...
T.D. Lukashova, M.G. Drushlyak
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Groups Factorized by Pairwise Permutable Abelian Subgroups of Finite Rank [PDF]
Advances in Group Theory and Applications, 2016 It is proved that a group which is the product of pairwise permutable abelian subgroups of finite Prüfer rank is hyperabelian with finite Prüfer rank; in the periodic case the Sylow subgroups of such a product are described.
Bernhard Amberg, Yaroslav P. Sysak
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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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