FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 1, PAGES 159-170

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

M. A. Roizner

Abstract

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We consider Abelian $p$-groups ($p$³
3) $A$_{1}
and $A$_{2} with nonzero
divisible parts.
In this paper, we prove that the automorphism groups $Aut\; A$_{1}
and $Aut\; A$_{2}
are elementarily equivalent if and only if the
groups $A$_{1}
and $A$_{2} are
equivalent in second-order logic.

Location: http://mech.math.msu.su/~fpm/eng/k13/k131/k13109h.htm

Last modified: September 5, 2013