Regular balanced Cayley maps on PSL(2,p)

A regular balanced Cayley map   (RBCM for short) on a finite group ΓΓ is an embedding of a Cayley graph on ΓΓ into a surface, with some special symmetric property. People have classified RBCM’s for cyclic, dihedral, generalized quaternion, dicyclic, and semi-dihedral groups. In this paper we classify RBCM’s on the group PSL(2,p) for each prime number p>3p>3.