Regular orbits of symmetric and alternating groups

© 2016 Elsevier Inc. Given a finite group G and a faithful irreducible FG-module V where F has prime order, does G have a regular orbit on V? This problem is equivalent to determining which primitive permutation groups of affine type have a base of size 2. In this paper, we classify the pairs (G, V) for which G has a regular orbit on V where G is a covering group of a symmetric or alternating group and V is a faithful irreducible FG-module such that the order of F is prime and divides the order of G.