K-theory of Solvable Groups

2002/07/17 by Tom Farrell, Farrell, Tom, Peter A. Linnell +2
Mathematics · #19B28 (Primary) #19G24 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:19B28 #msc:19G24

paper · pdf · doi:10.48550/arxiv.math/0207138

27 pages, Proc. London Math. Soc., to appear

arxiv created 2002/07/17 · openalex publication_date 2002/07/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first prove that the Whitehead group of a torsion-free virtually solvable linear group vanishes. Next we make a reduction of the fibered isomorphism conjecture from virtually solvable groups to a class of virtually solvable Q-linear groups. Finally we prove an L-theory analogue for elementary amenable groups.

Related

• Solvable fundamental groups of algebraic varieties and Kähler manifolds
• Solvable Quotients of Kahler Groups
• Solvable matrix groups and the Burnside problem
• Some torsion-free solvable groups with few subquotients
• Whitehead groups and the Bass conjecture