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Fundam. Prikl. Mat., 2012, Volume 17, Issue 5, Pages 157–163 (Mi fpm1440)  

This article is cited in 1 scientific paper (total in 1 paper)

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

M. A. Roizner

M. V. Lomonosov Moscow State University

Abstract: Consider reduced Abelian $p$-groups ($p\geq3$) $A_1$ and $A_2$. In this paper, we prove that the automorphism groups $\operatorname{Aut}A_1$ and $\operatorname{Aut}A_2$ are elementary equivalent if and only if the groups $A_1$ and $A_2$ are equivalent in second-order logic bounded by the cardinalities of the basic subgroups of $A_1$ and $A_2$.

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English version:
Journal of Mathematical Sciences (New York), 2013, 193:4, 586–590

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., 17:5 (2012), 157–163; J. Math. Sci., 193:4 (2013), 586–590

Citation in format AMSBIB
\Bibitem{Roi12}
\by M.~A.~Roizner
\paper A criterion of elementary equivalence of automorphism groups of reduced Abelian $p$-groups
\jour Fundam. Prikl. Mat.
\yr 2012
\vol 17
\issue 5
\pages 157--163
\mathnet{http://mi.mathnet.ru/fpm1440}
\transl
\jour J. Math. Sci.
\yr 2013
\vol 193
\issue 4
\pages 586--590
\crossref{https://doi.org/10.1007/s10958-013-1485-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899438505}


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    This publication is cited in the following articles:
    1. M. A. Roizner, “A criterion of elementary equivalence of automorphism groups of reduced Abelian $p$-groups”, J. Math. Sci., 201:4 (2014), 519–526  mathnet  crossref  mathscinet
  • Фундаментальная и прикладная математика
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