a1 Inst. Mittag-Leffler, Auravägen 17, 5-182 62 Djursholm, Sweden
a2 Department of Mathematical Sciences, University of Aberdeen, Aberdeen, Scotland
Let Σg denote a compact orientable surface of genus g ≥ 2. We consider finite groups G acting effectively on Σg and preserving the orientation—for short, G acts on Σg or Gis a symmetry group of Σg. Each surface Σg admits only finitely many symmetry groups G and the orders of these groups are bounded by Wiman's bound of 84(g – 1). This bound is attained for infinitely many values of g , see also , and all values of g ≤ 104 for which it is attained are known .
(Received January 31 1990)