Every coprime linear group admits a base of size two
Group Theory
2019-03-05 v2
Abstract
Let G be a linear group acting on the finite vector space V and assume that (|G|,|V|)=1. In this paper we prove that G has a base size at most two and this estimate is sharp. This generalizes and strengthens several former results concerning base sizes of coprime linear groups. As a direct consequence, we answer a question of I. M. Isaacs in the affirmative. Via large orbits this is related to the k(GV) theorem.
Cite
@article{arxiv.1212.0199,
title = {Every coprime linear group admits a base of size two},
author = {Zoltán Halasi and Károly Podoski},
journal= {arXiv preprint arXiv:1212.0199},
year = {2019}
}
Comments
Minor corrections. Theorem 5.9 and Remark 5.15 have been rephrased in a more general form