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arXiv · 1911.05785

Regular orbits of quasisimple linear groups I

Melissa Lee
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Abstract

Let $G \leq \mathrm{GL}(V)$ 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.

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Melissa Lee. 2019-11-13. Regular orbits of quasisimple linear groups I. https://arxiv.org/abs/1911.05785

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