Geodesic
Fully inert subgroups of completely decomposable groups, having homogeneous components of the final rank
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2022), pp. 91-100

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

For a considered class of completely decomposable torsion-free groups, comprising of itself all completely decomposable groups with final number homogeneous components, are found necessary and sufficient conditions, connected with types of component of the final rank, under which any fully inert subgroup commensurable with fully invariant. It is described of splitting mixed groups, in which any subgroup is projectively inert. It is shown that every projectively inert subgroups of the group form the sublattice in lattice of all its projectively inert subgroups.
Mots-clés : commensurable
Keywords: fully inert subgroup, projectively inert subgroup, uniformly projectively inert subgroup. 
A. R. Chekhlov. Fully inert subgroups of completely decomposable groups, having homogeneous components of the final rank. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2022), pp. 91-100. http://geodesic.mathdoc.fr/item/IVM_2022_12_a7/
@article{IVM_2022_12_a7,
     author = {A. R. Chekhlov},
     title = {Fully inert subgroups of completely decomposable groups, having homogeneous components of the final rank},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {91--100},
     year = {2022},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_12_a7/}
}
TY  - JOUR
AU  - A. R. Chekhlov
TI  - Fully inert subgroups of completely decomposable groups, having homogeneous components of the final rank
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2022
SP  - 91
EP  - 100
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/IVM_2022_12_a7/
LA  - ru
ID  - IVM_2022_12_a7
ER  - 
%0 Journal Article
%A A. R. Chekhlov
%T Fully inert subgroups of completely decomposable groups, having homogeneous components of the final rank
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2022
%P 91-100
%N 12
%U http://geodesic.mathdoc.fr/item/IVM_2022_12_a7/
%G ru
%F IVM_2022_12_a7

[1] Fuks L., Beskonechnye abelevy gruppy, v. 2, Mir, M., 1977

[2] Dardano U., Dikranjan D., Rinauro S., “Inertial properties in groups”, Int. J. Group theory, 7:3 (2018), 17–62

[3] Dardano U., Dikranjan D., Salce L., “On uniformly fully inert subgroups of abelian groups”, Topological Algebra and Appl., 8:1 (2020), 5–27

[4] Goldsmith B., Salce L., “Fully inert subgroups of torsion-complete $p$-groups”, J. Algebra, 555 (2020), 406–424

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

[6] Chekhlov A.R., Ivanets O.V., “O proektivno inertnykh podgruppakh vpolne razlozhimykh grupp konechnogo ranga”, Vestn. Tomsk. gos. un-ta, Ser. Matem. i mekh., 67 (2020), 63–68

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

[8] Chekhlov A.R., Danchev P.V., Goldsmith B., “On the socles of fully inert subgroups of Abelian $p$-groups”, Mediterranean J. Math., 18:3 (2021), 122–141