We prove that two elementarily equivalent Abelian p-groups with separable reduced parts are isotypically equivalent. Also as the corollary we prive that any Abelian p-group with a separable reduced part if ω-strongly homogeneous.
Annotation Consider unbounded reduced Abelian p-groups (p 3) A 1 and A 2 . In this paper, we prove that if the automorphism groups Aut A 1 and Aut A 2 are elementary equivalent then the groups A 1 and A 2 are equivalent in the second order logic bounded by the final rank of the basic subgroups of A 1 and A 2 .
We consider Abelian p-groups (p ≥ 3) A1 and A2 with nonzero divisible parts. In this paper, we prove that the automorphism groups Aut A1 and Aut A2 are elementarily equivalent if and only if the groups A1 and A2 are equivalent in second-order logic.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.