Abstract
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.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 7, pp. 81–112, 2009.
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Bunina, E.I., Roizner, M.A. Elementary equivalence of the automorphism groups of Abelian p-groups. J Math Sci 169, 614–635 (2010). https://doi.org/10.1007/s10958-010-0063-2
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DOI: https://doi.org/10.1007/s10958-010-0063-2