JournalsggdVol. 5, No. 2pp. 327–353

The congruence subgroup property for Aut F2F_2: A group-theoretic proof of Asada’s theorem

  • Kai-Uwe Bux

    Universität Bielefeld, Germany
  • Mikhail Ershov

    University of Virginia, Charlottesville, USA
  • Andrei S. Rapinchuk

    University of Virginia, Charlottesville, USA
The congruence subgroup property for Aut $F_2$:  A group-theoretic proof of Asada’s theorem cover
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Abstract

The goal of this paper is to give a group-theoretic proof of the congruence subgroup property for Aut(F2F_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(F2F_2).

Cite this article

Kai-Uwe Bux, Mikhail Ershov, Andrei S. Rapinchuk, The congruence subgroup property for Aut F2F_2: A group-theoretic proof of Asada’s theorem. Groups Geom. Dyn. 5 (2011), no. 2, pp. 327–353

DOI 10.4171/GGD/130