Quasi-finitely axiomatizable nilpotent groups

DOI10.1515/JGT.2006.005zbMath1121.20002MaRDI QIDQ5480158

Gabriel Sabbagh, Francis Oger

Publication date: 26 July 2006

Published in: Journal of Group Theory (Search for Journal in Brave)

zbMATH Keywords

finitely generated groupsprime modelsquasi-finitely axiomatizable nilpotent groups

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Model-theoretic algebra (03C60) Generators, relations, and presentations of groups (20F05) Nilpotent groups (20F18)

Related Items (13)

First-order rigidity of rings satisfying polynomial identities ⋮ Comparing quasi-finitely axiomatizable and prime groups ⋮ Full rank presentations and nilpotent groups: structure, Diophantine problem, and genericity ⋮ First order rigidity of non-uniform higher rank arithmetic groups ⋮ Polycyclic-by-finite groups and first-order sentences ⋮ A profinite analogue of Lasserre's theorem ⋮ Regular bi-interpretability of Chevalley groups over local rings ⋮ Bounded generation and commutator width of Chevalley groups: function case ⋮ On the model theory of higher rank arithmetic groups ⋮ Elementary equivalence of rings with finitely generated additive groups ⋮ Complete first-order theories of some classical matrix groups over algebraic integers ⋮ Prime and homogeneous rings and algebras ⋮ Quasi-finitely axiomatizable groups and groups which are prime models

Cites Work

• Équivalence élémentaire entre groupes finis-par-abéliens de type fini
• Elementary equivalence for abelian-by-finite and nilpotent groups
• Separating Classes of Groups by First-Order Sentences
• Cancellation and Elementary Equivalence of Finitely Generated Finite-By-Nilpotent Groups
• Elementary equivalence and genus of finitely generated nilpotent groups
• Elementary equivalence for finitely generated nilpotent groups and multilinear maps

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