Orbital Graphs for the Smallest Hurwitz Group

摘要

Hurwitz groups are the nontrivial finite quotients of the (2,3,7) triangle group (x,y= y~3= (xy)~7= 1>. In this paper we study the action of the smallest Hurwitz group is the simple group PSL(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.