Abstract:
The completely decomposable torsion-free Abelian groups with finitely many homogeneous components for which every fully inert subgroup is commensurable with a fully invariant subgroup are described.
Keywords:
fully inert subgroup, fully invariant subgroup, commensurable subgroups, completely decomposable group, index of a subgroup.
This publication is cited in the following 9 articles:
A. R. Chekhlov, “Fully inert subgroups of completely decomposable groups, having homogeneous components of the final rank”, Russian Math. (Iz. VUZ), 66:12 (2022), 82–90
Andrey R. Chekhlov, Peter V. Danchev, “Weakly fully and characteristically inert socle-regular Abelian p-groups”, Communications in Algebra, 50:11 (2022), 4975
Goldsmith B., Salce L., “Abelian P-Groups With Minimal Full Inertia”, Period. Math. Hung., 2021
A. R. Chekhlov, P. V. Danchev, B. Goldsmith, “On the socles of characteristically inert subgroups of abelian p-groups”, Forum Math., 33:4 (2021), 889–898
A. R. Chekhlov, P. V. Danchev, B. Goldsmith, “On the socles of fully inert subgroups of abelian p-groups”, Mediterr. J. Math., 18:3 (2021), 122
A. R. Chekhlov, O. V. Ivanets, “O proektivno inertnykh podgruppakh vpolne razlozhimykh grupp konechnogo ranga”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2020, no. 67, 63–68
U. Dardano, D. Dikranjan, S. Rinauro, “Inertial properties in groups”, Int. J. Group Theory, 7:3 (2018), 17–62
A. R. Chekhlov, “On Strongly Invariant Subgroups of Abelian Groups”, Math. Notes, 102:1 (2017), 106–110
A. R. Chekhlov, “Intermediately fully invariant subgroups of abelian groups”, Siberian Math. J., 58:5 (2017), 907–914