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=D₁ Å G₁ and $A$₂=D₂ Å G₂, 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.

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Last modified: April 18, 2010