论文标题
准线性线性组的常规轨道II
Regular orbits of quasisimple linear groups II
论文作者
论文摘要
令$ v $是有限的矢量空间，并假设$ g \ leqleqγ\ mathrm {l}（v）$是一个具有独特的quasisimple subgroup $ e（g）$的群体，在$ v $上绝对是不可记论的。 $ g $的基础是一组vectors $ b \ subseteq v $，带有尖端稳定器$ g_b = 1 $。如果$ g $的尺寸为1，我们说它在$ v $上具有常规轨道。在本文中，我们调查了$ e（g）/z（e（g））\ cong \ mathrm {psl} _n（q）$的最小基本大小，以定义特征，目的是将$ v $常规轨道的人分类。
Let $V$ be a finite-dimensional vector space over a finite field, and suppose $G \leq Γ\mathrm{L}(V)$ 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 $B\subseteq V$ 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 $E(G)/Z(E(G)) \cong \mathrm{PSL}_n(q)$ in defining characteristic, with an aim of classifying those with a regular orbit on $V$.
