The congruence subgroup property for $Aut F_2$: A group-theoretic proof of Asada's theorem

Details The congruence subgroup property for $Aut F_2$: A group-theoretic proof of Asada's theorem The congruence subgroup property for $Aut F_2$: A group-theoretic proof of Asada's theorem

2009-09-02

arxiv.org/abs/0909.0304v2

Groups, Geometry and Dynamics 5 (2011), no.2, 327-353

Mathematics

Group Theory

Final version

Scientific paper

10.4171/GGD/130

The 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 $Aut(F_2)$.

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