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Pré-Publication, Document De Travail Année : 2022

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.
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hal-03810038 , version 1 (11-10-2022)

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Adrien Le Boudec, Nicolás Matte Bon. Some torsion-free solvable groups with few subquotients. 2022. ⟨hal-03810038⟩
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