Geodesic
A criterion of elementary equivalence of automorphism groups of reduced Abelian $p$-groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 1, pp. 159-170

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We consider Abelian $p$-groups ($p\geq3$) $A_1$ and $A_2$ with nonzero divisible parts. In this paper, we prove that the automorphism groups $\operatorname{Aut}A_1$ and $\operatorname{Aut}A_2$ are elementarily equivalent if and only if the groups $A_1$ and $A_2$ are equivalent in second-order logic. 
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     author = {M. A. Roizner},
     title = {A criterion of elementary equivalence of automorphism groups of reduced {Abelian} $p$-groups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     publisher = {mathdoc},
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     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_1_a8/}
}
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M. A. Roizner. A criterion of elementary equivalence of automorphism groups of reduced Abelian $p$-groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 1, pp. 159-170. http://geodesic.mathdoc.fr/item/FPM_2013_18_1_a8/