Finite groups acting on almost all surfaces: Kulkarni revisited

Abstract

Kulkarni showed that a group G acts preserving orientation on the surfaceof genus g, for all but nitely many g, if and only if it is almost Sylow-cyclic with its Sylow 2-subgroup cyclic, dihedral, generalized quaternion, orgeneralized dicyclic. We generalize this result to non-orientable surfaces andorientation-reversing actions.