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- Title
On the abelianizations of congruence subgroups of Aut( F).
- Authors
Appel, Daniel
- Abstract
Let F be the free group of rank n, and let Aut( F) be its special automorphism group. For an epimorphism π : F → G of the free group F onto a finite group G we call $${\Gamma^+(G,\pi)=\{ \varphi \in {\rm Aut}^+(F_n) \mid \pi\varphi = \pi \}}$$ the standard congruence subgroup of Aut( F) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ( G, π) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Γ( G, π) ≤ Aut( F) has infinite abelianization.
- Subjects
AUTOMORPHISM groups; AUTOMORPHISMS; GROUP theory; FREE groups; ABELIAN groups
- Publication
Archiv der Mathematik, 2012, Vol 99, Issue 2, p101
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-012-0415-x