Geodesic
On Strongly Invariant Subgroups of Abelian Groups
Matematičeskie zametki, Tome 102 (2017) no. 1, pp. 125-132

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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
Mots-clés : socle of a group. 
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     author = {A. R. Chekhlov},
     title = {On {Strongly} {Invariant} {Subgroups} of {Abelian} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {125--132},
     publisher = {mathdoc},
     volume = {102},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a11/}
}
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A. R. Chekhlov. On Strongly Invariant Subgroups of Abelian Groups. Matematičeskie zametki, Tome 102 (2017) no. 1, pp. 125-132. http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a11/