3 problems

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Conjecture that every Abelian group belongs to the uniformly fully inert class
Abelian-group conjecture. The class $\mathcal{U}$ coincides with the class of all Abelian groups.
Theoremopenabelian-groups inert-subgroupsarXiv posted 2 days ago
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Dardano–Dikranjan–Rinauro–Salce conjecture for arbitrary groups
Dardano–Dikranjan–Rinauro–Salce conjecture. Every uniformly fully inert subgroup of $G$ is commensurable with a fully invariant subgroup of $G$ .
Conjectureopengroup-theory inert-subgroupsarXiv posted 2 days ago
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Dardano–Dikranjan–Rinauro–Salce conjecture on uniformly fully inert subgroups
Dardano–Dikranjan–Rinauro–Salce conjecture. Every uniformly fully inert subgroup of $G$ is commensurable with a fully invariant subgroup of $G$ .
Conjectureopenabelian-groups inert-subgroupsarXiv posted 2 days ago

Conjecture that every Abelian group belongs to the uniformly fully inert class