Abstract
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.
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