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A famous conjecture attributed to Dardano-Dikranjan-Rinauro-Salce states thatany uniformly fully inert subgroup of a given group is commensurable with afully invariant subgroup (see, respectively, [5] and [6]). In this short note,we completely settle this problem in the affirmative for an arbitrary Abeliangroup.

Solution to the Uniformly Fully Inert Subgroups Problem for Abelian Groups