A criterion of elementary equivalence of automorphism groups of reduced Abelian p-groups

Abstract

We consider Abelian p-groups (p ≥ 3) A1 and A2 with nonzero divisible parts. In this paper, we prove that the automorphism groups AutA1 and AutA2 are elementarily equivalent if and only if the groups A1 and A2 are equivalent in second-order logic.