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.
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Original Russian Text © A. R. Chekhlov, 2017, published in Matematicheskie Zametki, 2017, Vol. 102, No. 1, pp. 125–132.
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Chekhlov, A.R. On strongly invariant subgroups of Abelian groups. Math Notes 102, 105–110 (2017). https://doi.org/10.1134/S0001434617070112
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DOI: https://doi.org/10.1134/S0001434617070112