Alternating and symmetric groups as homomorphic images of G 3,11,m

Abstract

It is known that each conjugacy class of actions of PGL(2, Z) on projective line over the finite field, PL(F_q), can be represented by a coset diagram D(θ, q), where θ ∈ F_q and q is a power of a prime p. There are special types of fragments which occur frequently in D(θ, q). By using these diagrams and their fragments, we have proved that for a family of positive integers n = q + 1 = 2 + r + s, where r and s are primes, all alternating and symmetric groups of degree n occur as a homomorphic images of G^3,11,m where m = 2rs or m = 2r if r = s for some primes r and s.