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Fundam. Prikl. Mat., 2013, Volume 18, Issue 1, Pages 159–170 (Mi fpm1492)  

A criterion of elementary equivalence of automorphism groups of reduced Abelian $p$-groups

M. A. Roizner

Lomonosov Moscow State University, Moscow, Russia

Abstract: 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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English version:
Journal of Mathematical Sciences (New York), 2014, 201:4, 519–526

Bibliographic databases:

UDC: 512.541.6+510.67

Citation: M. A. Roizner, “A criterion of elementary equivalence of automorphism groups of reduced Abelian $p$-groups”, Fundam. Prikl. Mat., 18:1 (2013), 159–170; J. Math. Sci., 201:4 (2014), 519–526

Citation in format AMSBIB
\Bibitem{Roi13}
\by M.~A.~Roizner
\paper A criterion of elementary equivalence of automorphism groups of reduced Abelian $p$-groups
\jour Fundam. Prikl. Mat.
\yr 2013
\vol 18
\issue 1
\pages 159--170
\mathnet{http://mi.mathnet.ru/fpm1492}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431768}
\transl
\jour J. Math. Sci.
\yr 2014
\vol 201
\issue 4
\pages 519--526
\crossref{https://doi.org/10.1007/s10958-014-2008-7}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84906069350}


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