Solution to the Uniformly Fully Inert Subgroups Problem for Abelian Groups
Rings and Algebras
2024-01-02 v3 Group Theory
Abstract
A famous conjecture attributed to Dardano-Dikranjan-Rinauro-Salce states that any uniformly fully inert subgroup of a given group is commensurable with a fully invariant subgroup (see, respectively, [5] and [6]). In this short note, we completely settle this problem in the affirmative for an arbitrary Abelian group.
Cite
@article{arxiv.2307.15932,
title = {Solution to the Uniformly Fully Inert Subgroups Problem for Abelian Groups},
author = {Andrey R. Chekhlov and Peter V. Danchev},
journal= {arXiv preprint arXiv:2307.15932},
year = {2024}
}
Comments
We give a new very short proof of the crucial Proposition 2.2 and also provide more details in the proof of Proposition 2.3