Regular orbits of quasisimple linear groups I

[摘要] 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. (C) 2021 Published by Elsevier Inc.

[发布日期] 2021-11-15

[关键词] Base size;Groups of Lie type;Representation theory of quasisimple groups