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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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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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On T-Characterized Subgroups of Compact Abelian Groups
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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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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Coverings of Groups by Abelian Subgroups [PDF]
Canadian Journal of Mathematics, 1978 Paul Erdôs has suggested an investigation of infinite groups from the point of view of the partition relations of set theory. In particular, he suggested that given a group G, one considers the graph T with vertex set G whose edges are the pairs ﹛g, h﹜ which do not commute.
Vance Faber +2 more
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On finite 2-Groups with the non-Dedekind metacyclic norm of Abelian non-cyclic subgroups [PDF]
Advances in Group Theory and Applications, 2021 Tetiana D. Lukashova, Fedir M. Lyman
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SYLOW p-SUBGROUPS OF ABELIAN GROUP RINGS
, 2003 Let \(KG\) be the group ring of an Abelian group \(G\) over a commutative ring \(K\) and let \(V(KG)\) be the group of normalized units (i.e. the group of augmentation 1) in \(KG\). In the paper some group-theoretic properties of the \(p\)-component \(S(KG)\) of \(V(KG)\) are proved when either (i) \(K\) is a ring of prime characteristic \(p\) or (ii) \
Peter Danchev
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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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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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