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K ‐Theory of Solvable Groups
Author(s) -
Farrell F. Thomas,
Linnell Peter A.
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611503014072
Subject(s) - mathematics , solvable group , conjecture , isomorphism (crystallography) , pure mathematics , elementary theory , group isomorphism , class (philosophy) , torsion (gastropod) , combinatorics , discrete mathematics , outer automorphism group , automorphism group , automorphism , abelian group , medicine , chemistry , surgery , artificial intelligence , computer science , crystal structure , programming language , crystallography
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.