Abelian p-groups with minimal full inertia

Abstract The class of abelian p -groups with minimal full inertia, that is, satisfying the property fully inert subgroups are commensurable invariant is investigated, as well groups not this property; it known both direct sums cyclic and torsion-complete first type. It proved “small" endomorphism ring do satisfy concrete examples them provided via Corner’s realization theorems. Closure properties respect to two classes also studied. A topological condition socle a structural Jacobson radical -group G , which satisfied by groups, shown be independent having inertia. new subgroups, uniformly inert.