FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 7, PAGES 81-112

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

E. I. Bunina

M. A. Roizner

Abstract

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We consider Abelian $p$-groups ($p$³
3) $A$_{1}=D_{1} Å G_{1} and
$A$_{2}=D_{2} Å 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 $Aut\; A$_{1}
and $Aut\; A$_{2}
are elementarily equivalent, then the groups
$D$_{1}, $D$_{2} and
$G$_{1}, $G$_{2} are
equivalent, respectively, in the second-order logic.

Location: http://mech.math.msu.su/~fpm/eng/k09/k097/k09703h.htm

Last modified: April 18, 2010