Abstract
We continue the investigation started in [1]. Let be the Hurwitz space of coverings of degree of the projective line with Galois group and monodromy type . The monodromy type is a set of local monodromy types, which are defined as conjugacy classes of permutations in the symmetric group acting on the set . We prove that if the type contains sufficiently many local monodromies belonging to the conjugacy class of an odd permutation which leaves elements of fixed, then the Hurwitz space is irreducible.
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