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Fundam. Prikl. Mat., 2009, Volume 15, Issue 7, Pages 81–112 (Mi fpm1271)  

This article is cited in 3 scientific papers (total in 3 papers)

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

E. I. Bunina, M. A. Roizner

M. V. Lomonosov Moscow State University

Abstract: We consider Abelian $p$-groups ($p\geq3$) $A_1=D_1\oplus G_1$ and $A_2=D_2\oplus G_2$, where $D_1$ and $D_2$ are divisible and $G_1$ and $G_2$ are reduced subgroups. We prove that if the automorphism groups $\operatorname{Aut}A_1$ and $\operatorname{Aut}A_2$ are elementarily equivalent, then the groups $D_1$, $D_2$ and $G_1$, $G_2$ are equivalent, respectively, in the second-order logic.

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English version:
Journal of Mathematical Sciences (New York), 2010, 169:5, 614–635

Bibliographic databases:

UDC: 512.541.6+510.67

Citation: E. I. Bunina, M. A. Roizner, “Elementary equivalence of the automorphism groups of Abelian $p$-groups”, Fundam. Prikl. Mat., 15:7 (2009), 81–112; J. Math. Sci., 169:5 (2010), 614–635

Citation in format AMSBIB
\Bibitem{BunRoi09}
\by E.~I.~Bunina, M.~A.~Roizner
\paper Elementary equivalence of the automorphism groups of Abelian $p$-groups
\jour Fundam. Prikl. Mat.
\yr 2009
\vol 15
\issue 7
\pages 81--112
\mathnet{http://mi.mathnet.ru/fpm1271}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2745003}
\elib{http://elibrary.ru/item.asp?id=15340713}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 169
\issue 5
\pages 614--635
\crossref{https://doi.org/10.1007/s10958-010-0063-2}
\elib{http://elibrary.ru/item.asp?id=15329346}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77956059624}


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    Citing articles on Google Scholar: Russian citations, English citations
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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., 193:4 (2013), 586–590  mathnet  crossref
    2. 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
    3. M. A. Roizner, “Elementary equivalence of automorphism groups of reduced Abelian $p$-groups”, Moscow University Mathematics Bulletin, 68:3 (2013), 156–161  mathnet  crossref  mathscinet
  • Фундаментальная и прикладная математика
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