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Elementary equivalence for abelian-by-finite and nilpotent groups

Published online by Cambridge University Press:  12 March 2014

Francis Oger
Francis Oger*
Affiliation:
Équipe de Logique Mathématique, Université Paris, VII — C.N.R.S., 2 Place Jussieu — Case 7012, 75251 Paris Cédex 05, France, E-mail: oger@logique.jussieu.fr
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Abstract

We show that two abelian-by-finite groups are elementarily equivalent if and only if they satisfy the same sentences with two alternations of quantifiers. We also prove that abelian-by-finite groups satisfy a quantifier elimination property. On the other hand, for each integer n, we give some examples of nilpotent groups which satisfy the same sentences with n alternations of quantifiers and do not satisfy the same sentences with n + 1 alternations of quantifiers.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1471 - 1480
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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