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 Vestnik Moskov. Univ. Ser. 1. Mat. Mekh.: Year: Volume: Issue: Page: Find

 Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2013, Number 3, Pages 29–34 (Mi vmumm404)

Mathematics

Elementary equivalence of automorphism groups of reduced Abelian $p$-groups

M. A. Roizner

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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 $A_2$.

Key words: elementary equivalence, second order equivalence, Abelian $p$-groups, automorphism groups.

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English version:
Moscow University Mathematics Bulletin, 2013, 68:3, 156–161

Bibliographic databases:

UDC: 512.541.6 + 510.67

Citation: M. A. Roizner, “Elementary equivalence of automorphism groups of reduced Abelian $p$-groups”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2013, no. 3, 29–34; Moscow University Mathematics Bulletin, 68:3 (2013), 156–161

Citation in format AMSBIB
\Bibitem{Roi13} \by M.~A.~Roizner \paper Elementary equivalence of automorphism groups of reduced Abelian $p$-groups \jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh. \yr 2013 \issue 3 \pages 29--34 \mathnet{http://mi.mathnet.ru/vmumm404} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3185281} \transl \jour Moscow University Mathematics Bulletin \yr 2013 \vol 68 \issue 3 \pages 156--161 \crossref{https://doi.org/10.3103/S0027132213030042}