Generators for Alternating and Symmetric Groups

Abstract

Let Γ denote the modular group, that is, the free product of a group of order 2 and a group of order 3. Morris Newman investigates in [2] the factor-groups of Γ and calls them Γ-groups for short; thus a group is a Γ-group if and only if it has a generating set consisting of an element of order dividing 2 and an element of order dividing 3. Newman's interest centres on finite simple Γ-groups. He proves that the linear fractional groups LF(2,p) for primes p are Γ -groups, and poses the problem of deciding which of the alternating groups enjoy this property.