Some torsion-free solvable groups with few subquotients
Résumé
We construct finitely generated torsion-free solvable groups $G$ that have infinite rank, but such that all finitely generated torsion-free metabelian subquotients of $G$ are virtually abelian. In particular all finitely generated metabelian subgroups of $G$ are virtually abelian. The existence of such groups shows that there is no ``torsion-free version'' of P. Kropholler's theorem, which characterises solvable groups of infinite rank via their metabelian subquotients.
Domaines
Théorie des groupes [math.GR]
Origine : Fichiers produits par l'(les) auteur(s)