ON OVALS OF NON-CONJUGATE SYMMETRIES OF RIEMANN SURFACES

Abstract

We find the upper bound for the total number of ovals of k (5 ≤ k ≤ 8) non-conjugate symmetries of a Riemann surface of genus g, without an additional assumption concerning their separabilities, filling this way the gap existing in known literature of the subject. We also prove that our bound is attained for infinitely many values of g. Finally, as a byproduct of our considerations, we obtain the algebraic structure of the group generated by the extremal configurations of the symmetries, provided it is a 2-group.