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. 68, N 3, 2013.].
Unbounded reduced Abelian p-groups (p ≥ 3$) A1 and A2 are considered. It is proved that if the automorphism groups Aut A1 and Aut A2 are elementary equivalent, then the groups A1 and A2 are equivalent in the second order logic bounded with the final rank of the basic subgroups of A1 and A2.
Key words: elementary equivalence, second order equivalence, Abelian p-groups, automorphism groups.