On the index of congruence subgroups of Aut(Fn)

For an epimorphism of the free group Fn onto a finite group G we call Γ(G,π)={φ∈Aut(Fn)|πφ=π} the standard congruence subgroup of Aut(Fn) associated to G and π. In the case n=2 we present formulas for the index of Γ(G,π) where G is abelian or dihedral. Moreover, we show that congruence subgroups associated to dihedral groups provide a family of subgroups of arbitrary large index in Aut(F2) generated by a fixed number of elements. This implies that finite index subgroups of Aut(F2) cannot be written as free products.