A4, A5, S4 and S5 of schottky type

Abstract

Let H be a group of conformal automorphisms of a closed Riemann surface S, isomorphic to either of the alternating groups A4 or A5 or the symmetric groups S4 or S5. We provide necessary and sufficient conditions for the existence of a Schottky uniformization of S for which H lifts. In particular, togheter with the previous works in [3], [4] and [5], we exhaust the list of finite groups of M¨obius transformations of Schottky type.