, In this case the permutation s associated to the lift of the path around the branching point x can be seen as a bijection of the fiber G into itself. Let G be a group and fix an embedding i : G ? S ? . We say that a branched cover ? is a G-cover if every Hurwitz system for ? is in the image of i. By means of the embedding i we can construct checker surfaces associated to elements of G\G n /G. Furthermore, all the considerations above regarding S n -covers remain valid for general G-covers. In particular, the strong equivalence classes of G-covers are classified by the classes of homomorphisms of Hom

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