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.

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Last modified: September 5, 2013