FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 5, PAGES 157-163

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

M. A. Roizner

Abstract

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Consider reduced Abelian $p$-groups ($p$³
3) $A$_{1}
and $A$_{2}.
In this paper, we prove that the automorphism groups $Aut\; A$_{1}
and $Aut\; A$_{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}.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k115/k11510h.htm

Last modified: October 18, 2012