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Journal of Mathematical Sciences

, Volume 169, Issue 5, pp 614–635 | Cite as

Elementary equivalence of the automorphism groups of Abelian p-groups

  • E. I. Bunina
  • M. A. Roizner
Article

Abstract

We consider Abelian p-groups (p ≥ 3) A 1 = D 1G 1 and A 2 = D 2G 2, 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.

Keywords

Abelian Group Automorphism Group Cyclic Group Direct Summand Endomorphism Ring 
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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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