Elementary equivalence for abelian-by-finite and nilpotent groups
Copyright policy )Elementary equivalence for abelian-by-finite and nilpotent groups
AbstractWe 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.
- French National Centre for Scientific Research France
- Panthéon-Assas University France
- University of Paris France
- University of Paris France
Abelian-by-finite groups, Boolean rings, elementarily equivalent groups, Model-theoretic algebra, Applications of logic to group theory, Other classes of groups defined by subgroup chains, nilpotent groups, finitely generated groups, sentences, solvable groups
Abelian-by-finite groups, Boolean rings, elementarily equivalent groups, Model-theoretic algebra, Applications of logic to group theory, Other classes of groups defined by subgroup chains, nilpotent groups, finitely generated groups, sentences, solvable groups
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