Solution to the Uniformly Fully Inert Subgroups Problem for Abelian Groups

2023/07/29 by Chekhlov, Andrey R., Danchev, Peter V.
#20K10 #20K12 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2307.15932

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.

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