Completely Inert Subgroups of Abelian Groups
Group Theory
2025-04-08 v1 Commutative Algebra
Abstract
We define and study in-depth the so-called completely inert and uniformly completely inert subgroups of Abelian groups. We curiously show that a subgroup is completely inert exactly when it is characteristically inert. Moreover, we prove that a subgroup is uniformly completely inert precisely when it is uniformly characteristically inert. These two statements somewhat strengthen recent results due to Goldsmith-Salce established for totally inert subgroups in J. Commut. Algebra (2025). Some other closely relevant things are obtained as well.
Cite
@article{arxiv.2504.04111,
title = {Completely Inert Subgroups of Abelian Groups},
author = {Andrey R. Chekhlov and Peter V. Danchev},
journal= {arXiv preprint arXiv:2504.04111},
year = {2025}
}
Comments
12 pages