Abstract
Let V be a finite-dimensional vector space over a finite field, and suppose G≤ΓL(V) is a group with a unique subnormal quasisimple subgroup E(G) that is absolutely irreducible on V. A base for G is a set of vectors B⊆V with pointwise stabiliser GB=1. If G has a base of size 1, we say that it has a regular orbit on V. In this paper we investigate the minimal base size of groups G with E(G)/Z(E(G))≅PSLn(q) in defining characteristic, with an aim of classifying those with a regular orbit on V.
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