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- W2952178811 abstract "For an epimorphism pi of the free group F_n onto a finite group G write Gamma(G,pi) for the group of all automorphisms f of F_n for which pi*f = pi. This is called the standard congruence subgroup of Aut(F_n) associated to G and pi. In the case n = 2 we present formulas for the index of Gamma(G,pi) 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(F_2) generated by a fixed number of elements. This implies that finite index subgroups of Aut(F_2) cannot be written as free products." @default.
- W2952178811 created "2019-06-27" @default.
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- W2952178811 date "2008-04-16" @default.
- W2952178811 modified "2023-09-27" @default.
- W2952178811 title "On the Index of Congruence Subgroups of Aut(F_n)" @default.
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