Abstract:
We consider Abelian p-groups (p≥3) A1=D1⊕G1 and A2=D2⊕G2, where D1 and D2 are divisible and G1 and G2 are reduced subgroups. We prove that if the automorphism groups AutA1 and AutA2 are elementarily equivalent, then the groups D1, D2 and G1, G2 are equivalent, respectively, in the second-order logic.
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
\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://mathscinet.ams.org/mathscinet-getitem?mr=2745003}
\elib{https://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{https://elibrary.ru/item.asp?id=15329346}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77956059624}
Linking options:
https://www.mathnet.ru/eng/fpm1271
https://www.mathnet.ru/eng/fpm/v15/i7/p81
This publication is cited in the following 4 articles:
E. A. Blagoveshchenskaya, A. V. Mikhalev, “Influence of the Baer–Kaplansky theorem on the development of the theory of groups, rings, and modules”, J. Math. Sci., 269:5 (2023), 632–696
M. A. Roizner, “A criterion of elementary equivalence of automorphism groups of reduced Abelian p-groups”, J. Math. Sci., 201:4 (2014), 519–526
M. A. Roizner, “Elementary equivalence of automorphism groups of reduced Abelian p-groups”, Moscow University Mathematics Bulletin, 68:3 (2013), 156–161
M. A. Roizner, “A criterion of elementary equivalence of automorphism groups of reduced Abelian p-groups”, J. Math. Sci., 193:4 (2013), 586–590
Citation in format AMSBIB
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