Resolvents Of Certain Linear Groups In a Finite Field
L. Carlitz · Canadian Journal of Mathematics · 1956
Let Fq = GF(q) denote the finite field of order q = pn, where p is a prime. Consider the group Γ of linear transformations (1.1) x' = (ax + b)//(cx + d) with coefficients a, b, c, d ∊ Fq and of determinant 1. The order of Γ is ½q(q2 − 1) or q(q2 − 1) according as q is odd or even, i.e., according as p > 2 or p = 2.