Geodesic
The congruence subgroup property for Aut $F_2$: A group-theoretic proof of Asada’s theorem
Kai-Uwe Bux1 orcid ; Mikhail Ershov2 ; Andrei S. Rapinchuk2
1Universität Bielefeld, Germany
2University of Virginia, Charlottesville, USA
Groups, geometry, and dynamics, Tome 5 (2011) no. 2, pp. 327-353

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DOI

The goal of this paper is to give a group-theoretic proof of the congruence subgroup property for Aut(F2​), 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(F2​).
DOI : 10.4171/ggd/130
Classification : 20-XX, 00-XX
Mots-clés : Automorphism groups, free groups, congruence subgroup property

Kai-Uwe Bux  1   ; Mikhail Ershov  2   ; Andrei S. Rapinchuk  2

1 Universität Bielefeld, Germany
2 University of Virginia, Charlottesville, USA 
Kai-Uwe Bux; Mikhail Ershov; Andrei S. Rapinchuk. The congruence subgroup property for Aut $F_2$:  A group-theoretic proof of Asada’s theorem. Groups, geometry, and dynamics, Tome 5 (2011) no. 2, pp. 327-353. doi: 10.4171/ggd/130
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     title = {The congruence subgroup property for {Aut }$F_2$:  {A} group-theoretic proof of {Asada{\textquoteright}s} theorem},
     journal = {Groups, geometry, and dynamics},
     pages = {327--353},
     year = {2011},
     volume = {5},
     number = {2},
     doi = {10.4171/ggd/130},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/130/}
}
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