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arXiv · 0910.0090

On the Abelianization of Congruence Subgroups of Aut(F_2)

Daniel Appel
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Abstract

Let F_n be the free group of rank n and let Aut^+(F_n) be its special automorphism group. For an epimorphism pi : F_n -> G of the free group F_n onto a finite group G we call Gamma^+(G,pi) = {f in Aut^+(F_n) | pi*f = pi} the standard congruence subgroup of Aut^+(F_n) associated to G and pi. In the case n = 2 we fully describe the abelianization of Gamma^+(G,pi) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Gamma^+(G,pi) < Aut^+(F_2) has infinite abelianization.

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Daniel Appel. 2010-02-12. On the Abelianization of Congruence Subgroups of Aut(F_2). https://arxiv.org/abs/0910.0090

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