Abstract
We consider Abelian p-groups (p ≥ 3) A 1 and A 2 with nonzero divisible parts. In this paper, we prove that the automorphism groups AutA 1 and AutA 2 are elementarily equivalent if and only if the groups A 1 and A 2 are equivalent in second-order logic.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 1, pp. 159–170, 2013.
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Roizner, M.A. A Criterion of Elementary Equivalence of Automorphism Groups of Unreduced Abelian p-Groups. J Math Sci 201, 519–526 (2014). https://doi.org/10.1007/s10958-014-2008-7
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DOI: https://doi.org/10.1007/s10958-014-2008-7