Elementary equivalence of automorphism groups of reduced Abelian p-groups

Abstract

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 .

A Criterion of Elementary Equivalence of Automorphism Groups of Unreduced Abelian p-Groups

“…It is shown in [17] how to specify a basic subgroup B and to introduce structure on it. Precisely, there was introduced a formula stating that an indecomposable summand of A belongs to the group B and a set of automorphisms {g ij } was specified so that…”

“…According to [17], we say that an automorphism f a interprets an element a ∈ A if there is an element…”