Regular orbits of quasisimple linear groups I.

Let G ≤ GL (V) be a group with a unique subnormal quasisimple subgroup E (G) that acts absolutely irreducibly on V. A base for G acting on V is a set of vectors with trivial pointwise stabiliser in G. In this paper we determine the minimal base size of G when E (G) / Z (E (G)) is a finite simple group of Lie type in cross-characteristic. We show that G has a regular orbit on V , with specific exceptions, for which we find the base size. [ABSTRACT FROM AUTHOR]