Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 66, Issue 3 (2001), 1471-1480.
Elementary Equivalence for Abelian-by-Finite and Nilpotent Groups
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.
J. Symbolic Logic, Volume 66, Issue 3 (2001), 1471-1480.
First available in Project Euclid: 6 July 2007
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Oger, Francis. Elementary Equivalence for Abelian-by-Finite and Nilpotent Groups. J. Symbolic Logic 66 (2001), no. 3, 1471--1480. https://projecteuclid.org/euclid.jsl/1183746572