Some torsion-free solvable groups with few subquotients

2022/06/14 by Boudec, Adrien Le, Bon, Nicolás Matte
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2206.06689

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.

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• The cohomology of virtually torsion-free solvable groups of finite rank
• Solvable Subgroup Theorem for simplicial nonpositive curvature
• Non-solvable torsion-free virtually solvable groups
• The decomposability problem for torsion-free abelian groups is analytic complete