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K-Theory of Solvable Groups

Published online by Cambridge University Press:  01 October 2003

F. Thomas Farrell  and
Peter A. Linnell
F. Thomas Farrell
Affiliation:
Department of Mathematical Sciences, State University of New York at Binghamton, Binghamton, NY 13902-6000, USA. E-mail: farrell@math.binghamton.edu, www.math.binghamtom.edu/farrell/
Peter A. Linnell
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA. E-mail: linnell@math.vt.edu, www.math.vt.edu/people/linnell/
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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 $\mathbb {Q}$-linear groups. Finally we prove an L-theory analogue for elementary amenable groups.

Keywords

solvable groupWhitehead groupfibered isomorphism conjecture19B28 (primary)19G24 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 87 , Issue 2 , September 2003 , pp. 309 - 336
Copyright
2003 London Mathematical Society

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Footnotes

The first author was supported in part by the National Science Foundation.