International Conference on Advances in Natural and Applied Sciences (ICANAS), Antalya, Türkiye, 18 - 21 Nisan 2017, cilt.1833
Hurwitz groups are the nontrivial finite quotients of the (2, 3, 7) triangle group < x, y vertical bar x(2) = y(3) = (xy)(7) = 1 >. In this paper we study the action of the smallest Hurwitz group is the simple group PS L(2, 7) acts via linear fractional transformation on the projective line P-1(7) over the field by using directed suborbital graphs. We obtain edge and circuit conditions.