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.

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