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In this note we consider a class of groups of conformal 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 ≥ 2 is the genus of the surface. We also describe a sequence of infinite genera g1 < g2 < · · · for which these upper bound is attained. Also lower bounds are found, for instance, (i) 4(g+1) for even genus and 8(g−1) for odd genus. Also, for cyclic groups in such a family sharp upper bounds are given.

BOUNDS FOR CONFORMAL AUTOMOMORPHISMS OF RIEMANN SURFACES WITH CONDITION (A)