Elementary Equivalence and Profinite Completions: A Characterization of Finitely Generated Abelian-by-Finite Groups

DOI10.2307/2047082zbMath0642.20001OpenAlexW4252840410MaRDI QIDQ3784297

Francis Oger

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2047082

zbMATH Keywords

profinite completionelementary submodelelementarily equivalentfinitely generated abelian-by- finite groupsfinitely generated nilpotent-by- finite group

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Model-theoretic algebra (03C60) Generalizations of solvable and nilpotent groups (20F19) Limits, profinite groups (20E18)

Related Items (6)

Elementary equivalence of a polycyclic-by-finite group and its profinite completion ⋮ Direct products and elementary equivalence of polycyclic-by-finite groups. ⋮ Commensurability and elementary equivalence of polycyclic groups ⋮ Finite images and elementary equivalence of completely regular inverse semigroups ⋮ Quasi-finitely axiomatizable groups and groups which are prime models ⋮ Elementary equivalence for finitely generated nilpotent groups and multilinear maps

Cites Work

• Équivalence élémentaire entre groupes finis-par-abéliens de type fini
• The cancellation of an infinite cyclic group in direct products
• Genus and cancellation for groups with finite commutator subgroups
• Nilpotent groups
• Model theory
• The model theory of finitely generated finite-by-abelian groups
• The Equivalence of × t C ≈× t D and J × C ≈J × D
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