Elementary equivalence of the automorphism groups of Abelian p-groups

E. I. Bunina; M. A. Roizner

doi:10.1007/s10958-010-0063-2

Elementary equivalence of the automorphism groups of Abelian p-groups

E. I. Bunina, M. A. Roizner

Lomonosov Moscow State University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We consider Abelian p-groups (p ≥ 3) A₁ = D₁ ⊕ G₁ and A₂ = D₂ ⊕ G₂, where D₁ and D₂ are divisible and G₁ and G₂ are reduced subgroups. We prove that if the automorphism groups Aut A₁ and Aut A₂ are elementarily equivalent, then the groups D₁, D₂ and G₁, G₂ are equivalent, respectively, in the second-order logic.

Original language	English
Pages (from-to)	614-635
Number of pages	22
Journal	Journal of Mathematical Sciences
Volume	169
Issue number	5
DOIs	https://doi.org/10.1007/s10958-010-0063-2
State	Published - 2010
Externally published	Yes

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AB - We consider Abelian p-groups (p ≥ 3) A1 = D1 ⊕ G1 and A2 = D2 ⊕ G2, where D1 and D2 are divisible and G1 and G2 are reduced subgroups. We prove that if the automorphism groups Aut A1 and Aut A2 are elementarily equivalent, then the groups D1, D2 and G1, G2 are equivalent, respectively, in the second-order logic.

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Elementary equivalence of the automorphism groups of Abelian p-groups

Abstract

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