Regular orbits of quasisimple linear groups II

2020/06/26 by Lee, Melissa
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2006.14954

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 G_B=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)) ≅ PSL_n(q) in defining characteristic, with an aim of classifying those with a regular orbit on V.

Related

• Regular orbits of quasisimple linear groups I
• Regular orbits of finite primitive solvable groups, III
• Absolutely irreducible quasisimple linear groups containing elements of order a specified Zsigmondy prime
• Regular orbits and p-regular orbits of solvable linear groups
• Regular orbits of coprime linear groups in large characteristic