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The genus of PSl2 (q).

In [3] we computed the genus of the linear fractional group PS/2(p), where p*z5 is a prime. That is, we determined the least integer g such that PSl2(p) could occur äs an effective group of orientation preserving symmetries of Sg9 the closed orientable surface of genus g. More generally, given any finite group G we define the genus of G to be the least integer g so that G acts effectively and orientably on Sg. There is no loss of generality if we require the actions to be conformal, that is analytic in some complex structure on Sg9 since the positive solution of the Nielsen Realization Problem by [4], [2] implies that if G acts topologically on Sg then it can also act conformally with respect to some complex structure.