Kai-Uwe Bux
The congruence subgroup property for $Aut F_2$: A group-theoretic proof of Asada's theorem.
Thu, 09/03/2009 - 17:38 — SomNambulAuthors: Mikhail Ershov, Kai-Uwe Bux, Andrei Rapinchuk
Subjects: Group Theory
AbstractThe goal of this paper is to give a group-theoretic proof of the congruence
subgroup property for $Aut(F_2)$, the group of automorphisms of a free group on
two generators. This result was first proved by Asada using techniques from
anabelian geometry, and our proof is, to a large extent, a translation of
Asada's proof into group-theoretic language. This translation enables us to
simplify many parts of Asada's original argument and prove a quantitative
version of the congruence subgroup property for $Aut(F_2)$.Finiteness Properties of Chevalley Groups over a Polynomial Rings over a Finite Field.
Tue, 09/01/2009 - 12:47 — SomNambulAuthors: Kai-Uwe Bux, Ralf Gramlich, Stefan Witzel
Subjects: Group Theory
AbstractIt is known from work by H. Abels and P. Abramenko that for a classical
Fq-group G of rank n the arithemetic lattice G(Fq[t]) of Fq[t]-rational points
is of type Fn-1 provided that q is large enough. We show that the statement is
true without any assumption on q and for any isotropic, absolutely almost
simple group G defined over Fq.
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