ELEMENTARY EQUIVALENCE OF THE AUTOMORPHISM GROUPS OF ABELIAN p-GROUPS

摘要

We consider Abelian p-groups (p≥3) A_1= D_1⊕G_1 and A_2 = D_2⊕G_2, where D_1 and D_2 are divisible and G_1 and G_2 are reduced subgroups. We prove that if the automorphism groups Aut A_1 and Aut A_2 are elementarily equivalent, then the groups D_1, D_2 and G_1, G_2 are equivalent, respectively, in the second-order logic.