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arXiv · 0909.0304

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

Kai-Uwe Bux·Mikhail Ershov·Andrei Rapinchuk
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Abstract

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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Kai-Uwe Bux, Mikhail Ershov, Andrei Rapinchuk. 2009-09-02. The congruence subgroup property for $Aut F_2$: A group-theoretic proof of Asada's theorem. https://doi.org/10.4171/ggd/130

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