Elementary Equivalence for Abelian-by-Finite and Nilpotent Groups

Journal of Symbolic Logic 66 (3):1471-1480 (2001)
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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.

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Diophantine Induction.Richard Kaye - 1990 - Annals of Pure and Applied Logic 46 (1):1-40.
The model theory of unitriangular groups.Oleg V. Belegradek - 1994 - Annals of Pure and Applied Logic 68 (3):225-261.
Axiomatization of abelian-by- G groups for a finite group G.Francis Oger - 2001 - Archive for Mathematical Logic 40 (7):515-521.

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