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- Title
Some torsion-free solvable groups with few subquotients.
- Authors
LE BOUDEC, ADRIEN; MATTE BON, NICOLÁS
- Abstract
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.
- Subjects
SOLVABLE groups; INFINITE groups; FREE groups; TORSION theory (Algebra)
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2024, Vol 176, Issue 2, p279
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004123000506