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 Mat. Zametki, 2017, Volume 102, Issue 1, Pages 125–132 (Mi mz11362)

On Strongly Invariant Subgroups of Abelian Groups

A. R. Chekhlov

Tomsk State University

Abstract: It is shown that every homogeneous separable torsion-free group is strongly invariant simple (i.e., has no nontrivial strongly invariant subgroups) and, for a completely decomposable torsion-free group, every strongly invariant subgroup coincides with some direct summand of the group. The strongly invariant subgroups of torsion-free separable groups are described. In a torsion-free group of finite rank, every strongly inert subgroup is commensurable with some strongly invariant subgroup if and only if the group is free. The periodic groups, torsion-free groups, and split mixed groups in which every fully invariant subgroup is strongly invariant are described.

Keywords: fully invariant subgroups, strongly invariant subgroups, strongly inert subgroups, commensurable subgroups, index of a subgroup, strongly invariant simple group, rank of a group, socle of a group.

DOI: https://doi.org/10.4213/mzm11362

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English version:
Mathematical Notes, 2017, 102:1, 106–110

Bibliographic databases:

UDC: 512.541

Citation: A. R. Chekhlov, “On Strongly Invariant Subgroups of Abelian Groups”, Mat. Zametki, 102:1 (2017), 125–132; Math. Notes, 102:1 (2017), 106–110

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz11362
• https://doi.org/10.4213/mzm11362
• http://mi.mathnet.ru/eng/mz/v102/i1/p125

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This publication is cited in the following articles:
1. A. R. Chekhlov, “Intermediately fully invariant subgroups of abelian groups”, Siberian Math. J., 58:5 (2017), 907–914
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