Geodesic
Elementary equivalence of automorphism groups of reduced Abelian $p$-groups
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 29-34

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Unbounded reduced Abelian $p$-groups ($p\geq3$) $A_1$ and $A_2$ are considered. It is proved that if the automorphism groups $\operatorname{Aut}A_1$ and $\operatorname{Aut}A_2$ 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 $A_2$. 
@article{VMUMM_2013_3_a3,
     author = {M. A. Roizner},
     title = {Elementary equivalence of automorphism groups of reduced {Abelian} $p$-groups},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {29--34},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a3/}
}
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M. A. Roizner. Elementary equivalence of automorphism groups of reduced Abelian $p$-groups. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 29-34. http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a3/