### SK_1 like functors for division algebras, by Roozbeh Hazrat

We investigate the group valued functor G(D)=D^*/F^*D' where D is a division
algebra with center F and D' the commutator subgroup of D^*. We show that G
has the most important functorial properties of the reduced Whitehead group
SK_1. We then establish a fundemental connection between this group, its
residue version and relative value group when D is a Henselian division
algebra. The structure of G(D) turns out to carry significant information
about the arithmetic of D. Along these lines, we employ G(D) to compute the
group SK_1(D). As an application, we obtain theorems of reduced K-theory
which require heavy machinery, as simple examples of our method.

Roozbeh Hazrat <rhazrat@mathematik.uni-bielefeld.de>