Elementary equivalence of automorphism groups of reduced Abelian *p*-groups / *M. A. Royzner.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2013. № 3. P. 29-34
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

Unbounded reduced Abelian *p*-groups (*p* ≥ 3$) *A*_{1} and *A*_{2} are considered. It is proved 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 with the final rank of the basic subgroups of *A*_{1} and *A*_{2}.

*Key words*:
elementary equivalence, second order equivalence, Abelian *p*-groups, automorphism groups.