论文标题
几乎没有简单的零星组可以原始作用于广义四边形的点
No almost simple sporadic group acts primitively on the points of a generalised quadrangle
论文作者
论文摘要
广义四边形是点线的入射率GOMETRY g，因此：（i）任何两个点最多位于一条线上，并且（ii）给定L和一个点p不与L一起入射，在L colinear上与p有独特的点。它们是山雀引入的广义多边形的特定案例，这些结构及其自动形态组在有限的几何形状中至关重要。理解有限广义四边形的自动形态群体的一个不可或缺的一部分是知道哪些群体可以原始作用在其观点上，尤其是几乎简单的群体作为自动形态群体出现。我们表明，几乎没有简单的零星组可以原始作用在有限的（厚）广义四边形的点上。我们还提出了两个新的想法，这些想法是为分析针对广义四边形的积分主要群体的贡献。首先是用于确定给定组是否可以原始作用在某些广义四边形点的算法的轮廓和实现。第二个是对这项工作过程中观察结果产生的猜想的讨论：任何对广义四边形点上作用原始作用的群体都必须在线上进行延伸或恰好具有两个线路孔，每个线均包含一半的线。
A generalised quadrangle is a point-line incidence geometry G such that: (i) any two points lie on at most one line, and (ii) given a line L and a point p not incident with L, there is a unique point on L collinear with p. They are a specific case of the generalised polygons introduced by Tits, and these structures and their automorphism groups are of some importance in finite geometry. An integral part of understanding the automorphism groups of finite generalised quadrangles is knowing which groups can act primitively on their points, and in particular, which almost simple groups arise as automorphism groups. We show that no almost simple sporadic group can act primitively on the points of a finite (thick) generalised quadrangle. We also present two new ideas contributing towards analysing point-primitive groups acting on generalised quadrangles. The first is the outline and implementation of an algorithm for determining whether a given group can act primitively on the points of some generalised quadrangle. The second is the discussion of a conjecture resulting from observations made in the course of this work: any group acting primitively on the points of a generalised quadrangle must either act transitively on lines or have exactly two line-orbits, each containing half of the lines.
