2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79650In this paper we determine all finite groups G that can act on some compact Riemann surface M with the property that if H is any non-trivial subgroup of G, then the orbit surface M/H is the Riemann sphere. The idea is to look at the induced action on the vector space of holomorphic differentials on M (in the positive genus case) and then use the old-known (Wolf) classification of groups admitting fixed point-free linear actions. A description of the corresponding group actions is given in terms of Fuchsian representations.21 pages, 5 figuresAlgebraic Geometrytext