Abstract

In this work, we study the monodromy group of covers phi circle psi of curves Y ->(psi) X ->(phi) P-1, where psi is a q-fold cyclic etale cover and phi is a totally ramified p-fold cover, with p and q different prime numbers with p odd. We show that the Galois group G of the Galois closure Z of phi circle psi is of the form G = Z(q)(s) (sic) U, where 0 = s = p - 1 and U is a simple transitive permutation group of degree p. Since the simple transitive permutation group of prime degree p are known, and we construct examples of such covers with these Galois groups, the result is very different from the previously known case when the cover phi was assumed to be cyclic, in which case the Galois group is of the form G = Z(q)(s) (sic) Z(p). Furthermore, we are able to characterize the subgroups H and N of G such that Y = Z/N and X = Z/H.