论文标题
极端原始的群体和线性空间
Extremely primitive groups and linear spaces
论文作者
论文摘要
如果点稳定器在其每个非平凡轨道上都作用，则有限的非规范置换组$ g $是极其原始的。此类群体已经研究了将近一个世纪，发现了各种应用。 Burness和Lee最近完成了极端原始群体的分类，他们依靠Mann，Praeger和Seress对可溶性极具原始群体的早期分类。不幸的是，后一种分类存在不准确。我们纠正了这个错误，还研究了常规的线性空间，这些线性空间允许在点上极为原始的自动形态。
A finite non-regular primitive permutation group $G$ is extremely primitive if a point stabiliser acts primitively on each of its nontrivial orbits. Such groups have been studied for almost a century, finding various applications. The classification of extremely primitive groups was recently completed by Burness and Lee, who relied on an earlier classification of soluble extremely primitive groups by Mann, Praeger and Seress. Unfortunately, there is an inaccuracy in the latter classification. We correct this mistake, and also investigate regular linear spaces which admit groups of automorphisms that are extremely primitive on points.
