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Elementary equivalence for abelian-by-finite and nilpotent groups
Published online by Cambridge University Press: 12 March 2014
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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- Copyright © Association for Symbolic Logic 2001
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