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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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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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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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Non-periodic groups with the restrictions on the norm of cyclic subgroups of non-prime order
Математичні Студії, 2022 One of the main directions in group theory is the study of the impact of characteristic subgroups on the structure of the whole group. Such characteristic subgroups include different $\Sigma$-norms of a group.
M. Drushlyak, T. Lukashova
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On the Structure of Groups whose Non-Abelian Subgroups are Serial [PDF]
Advances in Group Theory and Applications, 2016 Necessary and sufficient conditions are given for a locally finite group to have all non-abelian subgroups serial. We also obtain results for groups whose non-abelian subgroups are permutable.
M.R. Dixon, L.A. Kurdachenko, N.N. Semko
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Influence of complemented subgroups on the structure of finite groups [PDF]
International Journal of Group Theory, 2021 P. Hall proved that a finite group $G$ is supersoluble with elementary abelian Sylow subgroups if and only if every subgroup of $G$ is complemented in $G$. He called such groups complemented. A. Ballester-Bolinches and X.
Izabela Malinowska
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Normalizers and centralizers of subgroups in non-Abelian groups of small order [PDF]
Компьютерные исследования и моделирование, 2012 By applying the computer program, which is created by authors, we obtain the exact representation of normalizers and centralizers of all nontrivial subgroups in non-Abelian groups G under the condition |G|20.
Ilya Anatolievih Shilin +1 more
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On uniformly fully inert subgroups of abelian groups
Topological Algebra and its Applications, 2020 If H is a subgroup of an abelian group G and φ ∈ End(G), H is called φ-inert (and φ is H-inertial) if φ(H) ∩ H has finite index in the image φ(H). The notion of φ-inert subgroup arose and was investigated in a relevant way in the study of the so called ...
Dardano Ulderico +2 more
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