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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2017_102_1_a11,
     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/}
}
TY  - JOUR
AU  - A. R. Chekhlov
TI  - On Strongly Invariant Subgroups of Abelian Groups
JO  - Matematičeskie zametki
PY  - 2017
SP  - 125
EP  - 132
VL  - 102
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a11/
LA  - ru
ID  - MZM_2017_102_1_a11
ER  - 
%0 Journal Article
%A A. R. Chekhlov
%T On Strongly Invariant Subgroups of Abelian Groups
%J Matematičeskie zametki
%D 2017
%P 125-132
%V 102
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a11/
%G ru
%F MZM_2017_102_1_a11
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/

[1] G. Călugăreanu, “Strongly invariant subgroups”, Glasg. Math. J., 57:2 (2015), 431–443 | DOI | MR | Zbl

[2] D. Dikranjan, A. Giordano Bruno, L. Salce, S. Virili, “Fully inert subgroups of divisible Abelian groups”, J. Group Theory, 16:6 (2013), 915–939 | DOI | MR | Zbl

[3] D. Dikranjan, L. Salce, P. Zanardo, “Fully inert subgroups of free Abelian groups”, Period. Math. Hungar, 69:1 (2014), 69–78 | DOI | MR | Zbl

[4] B. Goldsmith, L. Salce, P. Zanardo, “Fully inert subgroups of Abelian $p$-groups”, J. Algebra, 419 (2014), 332–349 | DOI | MR | Zbl

[5] A. R. Chekhlov, “Vpolne inertnye podgruppy vpolne razlozhimykh grupp konechnogo ranga i ikh soizmerimost”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2016, no. 3 (41), 42–50 | DOI

[6] A. R. Chekhlov, “O vpolne inertnykh podgruppakh vpolne razlozhimykh grupp”, Matem. zametki, 101:2 (2017), 302–312 | DOI | MR

[7] A. R. Chekhlov, P. V. Danchev, “On abelian groups having all proper fully invariant subgroups isomorphic”, Comm. Algebra, 43:12 (2015), 5059–5073 | DOI | MR | Zbl