A note on uniformly totally strongly inert subgroups of Abelian groups

Andrey R. Chekhlov^a, Peter V. Danchev^b, Patrick W. Keef<sup>c

a</sup> Faculty of Mathematics and Mechanics, Tomsk State University, Tomsk, Russian Federation
^b Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
^c Department of Mathematics, Whitman College, Walla Walla, WA, Unites States

Abstract: We prove in this short note that any uniformly totally inert subgroup of a given group is commensurable with a uniformly fully invariant subgroup of the whole group as well as that any uniformly totally strongly inert subgroup is commensurable with a strongly invariant subgroup, thus somewhat extending results due to Breaz–Cǎlugǎreanu in Rend. Sem. Mat. Univ. Padova (2017), Chekhlov–Danchev in Rocky Mount. J. Math. (2025) and Goldsmith–Salce in J. Comm. Algebra (2025).

Keywords: Abelian groups, (characteristically, fully, strongly) invariant subgroups, uniformly (characteristically, fully, totally) inert subgroups.

UDC: 512.5

Received: 11.11.2024
Received in revised form: 17.01.2025
Accepted: 24.02.2025

Language: English