Triviality of the reduced Whitehead group over certain fields

1978 ◽  
Vol 24 (5) ◽  
pp. 836-841
Author(s):  
V. A. Lipnitskii
Keyword(s):  
Whitehead Group

A Geometric Construction of the Boundedly Controlled Whitehead Group

2020 ◽  
pp. 13-26
Author(s):  
Douglas R. Anderson ◽  
Hans Jørgen Munkholm
Keyword(s):  
Geometric Construction ◽  
Whitehead Group

scholarly journals The Whitehead group of a polynomial extension

1964 ◽  
Vol 22 (1) ◽  
pp. 61-79 ◽  
Author(s):  
H. Bass ◽  
A. Heller ◽  
R. G. Swan
Keyword(s):  
Whitehead Group ◽  
Polynomial Extension

scholarly journals Homotopy invariance of non-stable K1-functors

2013 ◽  
Vol 13 (2) ◽  
pp. 199-248 ◽  
Author(s):  
A. Stavrova
Keyword(s):  
Normal Subgroup ◽  
Algebraic Group ◽  
Whitehead Group ◽  
Homotopy Invariance ◽  
Reductive Algebraic Group ◽  
Rank 2

AbstractLet G be a reductive algebraic group over a field k, such that every semisimple normal subgroup of G has isotropic rank ≥ 2, i.e. contains (Gm)2. Let K1G be the non-stable K1-functor associated to G, also called the Whitehead group of G. We show that K1G(k) = K1G (k[X1 ,…, Xn]) for any n ≥ 1. If k is perfect, this implies that K1G (R) = K1G (R[X]) for any regular k-algebra R. If k is infinite perfect, one also deduces that K1G (R) → K1G (K) is injective for any local regular k-algebra R with the fraction field K.

scholarly journals A non-reflexive Whitehead group

2001 ◽  
Vol 156 (2-3) ◽  
pp. 199-214 ◽  
Author(s):  
Paul C. Eklof ◽  
Saharon Shelah
Keyword(s):  
Whitehead Group

scholarly journals Unitary Whitehead group of cyclic groups

1974 ◽  
Vol 28 (3) ◽  
pp. 461-476 ◽  
Author(s):  
Man Keung Siu
Keyword(s):  
Whitehead Group ◽  
Cyclic Groups
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