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arXiv · 2504.04111

Completely Inert Subgroups of Abelian Groups

Andrey R. Chekhlov·Peter V. Danchev
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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.

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BibTeXRIS

Andrey R. Chekhlov, Peter V. Danchev. 2025-04-05. Completely Inert Subgroups of Abelian Groups. https://arxiv.org/abs/2504.04111

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