Isotypic equivalence of Abelian $p$-groups with separable reduced parts - Bunina, Elena (Sarajevo Journal of Mathematics, 2024)
We prove that two Abelian $p$-groups with separable reduced parts are isotypically equivalent if and only if their divisible parts and their basic subgroups are elementarily equivalent. Also as a corollary we prove that any Abelian $p$-group with a separable reduced part is $ω$-strongly homogeneous