Abstract

In this note we consider a class of groups of conformai automorphisms of closed Riemann surfaces containing those which can be lifted to some Schottky uniformization. These groups are those which satisfy a necessary condition for the Schottky lifting property. We find that all these groups have upper bound 12(g -1), where g ? 1 is the genus of the surface. We also describe a sequence of infinite genera g1 < 02 < ? for which these upper bound is attained. Also lower bounds are found, for instancei) 4(0 + 1) for even genus and 8(g-1) for odd genus. Also, for cyclic groups in such a family sharp upper bounds are given.