The goal of this paper is to give a group-theoretic proof of the congruence subgroup property for Aut(), 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().
Cite this article
Kai-Uwe Bux, Mikhail Ershov, Andrei S. Rapinchuk, The congruence subgroup property for Aut : A group-theoretic proof of Asada’s theorem. Groups Geom. Dyn. 5 (2011), no. 2, pp. 327–353DOI 10.4171/GGD/130