论文标题
点主要的概括性六角形和八幅和投影线性群
Point-primitive generalised hexagons and octagons and projective linear groups
论文作者
论文摘要
我们讨论了分类点主要的广义多边形问题的最新进展。就广义六角形和广义八幅而言，这将问题降低为几乎简单的谎言类型的原始作用。为了说明这些群体的自然几何形状如何在这项研究中使用，我们表明，如果$ \ nathcal {s} $是有限的厚实的六角形或八角形，带有$ g \ leqslant {\ rm aut}（\ rm aut}（\ nathcal {s}}） psl} _n（q）$，其中$ n \ geqslant 2 $，然后点的稳定器在天然模块上不可总比行为。我们描述了一种策略，以证明这种广义的六边形或八角形$ \ Mathcal {s} $不存在。
We discuss recent progress on the problem of classifying point-primitive generalised polygons. In the case of generalised hexagons and generalised octagons, this has reduced the problem to primitive actions of almost simple groups of Lie type. To illustrate how the natural geometry of these groups may be used in this study, we show that if $\mathcal{S}$ is a finite thick generalised hexagon or octagon with $G \leqslant{\rm Aut}(\mathcal{S})$ acting point-primitively and the socle of $G$ isomorphic to ${\rm PSL}_n(q)$ where $n \geqslant 2$, then the stabiliser of a point acts irreducibly on the natural module. We describe a strategy to prove that such a generalised hexagon or octagon $\mathcal{S}$ does not exist.
