(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.

Location: http://mech.math.msu.su/~fpm/eng/k09/k097/k09703h.htm
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