---
res:
bibo_abstract:
- 'Let G and E stand for one of the following pairs of groups: Either G is the general
quadratic group U(2n, R, Lambda), n >= 3, and E its elementary subgroup EU(2n,
R, Lambda). for an almost commutative form ring (R, Lambda). or G is the Chevalley
group G(Phi, R) of type Phi, and E its elementary subgroup E(Phi, R), where Phi
is a reduced irreducible root system of rank >= 2 and R is commutative. Using
Bak''s localization-completion method in [A. Bak, Nonabelian K-theory: The nilpotent
class of K, and general stability, K-Theory 4 (4) (1991) 363-397], it was shown
in [R. Hazrat, Dimension theory and nonstable K-1 of quadratic modules, K-Theory
514 (2002) 1-35 and R. Hazrat, N. Vavilov, K-1 of Chevalley groups are nilpotent,
J. of Pure and Appl. Algebra 179 (2003) 99-116] that G/E is nilpotent by abelian,
when R has finite Bass-Serre dimension. In this note, we combine localization-completion
with a version of Stein''s relativization [M.R. Stein, Relativizing functors on
rings and algebraic K-theory, J. Algebra 19 (1) (1971) 140-152], which is applicable
to our situation [A. Bak, N. Vavilov, Structure of hyperbolic unitary groups I,
Elementary subgroups. Algebra Colloq. 7 (2) (2000) 159-196], and carry over the
results in the latter of the two references cited above to the relative case.
In other words, we prove that not only absolute K, functors, but also the relative
K, functors, are nilpotent by abelian. (C) 2008 Elsevier B.V. All rights reserved.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Anthony
foaf_name: Bak, Anthony
foaf_surname: Bak
foaf_workInfoHomepage: http://www.librecat.org/personId=10484
- foaf_Person:
foaf_givenName: Roozbeh
foaf_name: Hazrat, Roozbeh
foaf_surname: Hazrat
- foaf_Person:
foaf_givenName: N.
foaf_name: Vavilov, N.
foaf_surname: Vavilov
bibo_doi: 10.1016/j.jpaa.2008.11.014
bibo_issue: '6'
bibo_volume: 213
dct_date: 2009^xs_gYear
dct_identifier:
- UT:000264415800015
dct_isPartOf:
- http://id.crossref.org/issn/0022-4049
dct_language: eng
dct_title: 'Localization-completion strikes again: Relative K-1 is nilpotent by
abelian@'
...