论文标题
关于极端原始仿射组的注释
A note on extremely primitive affine groups
论文作者
论文摘要
令$ g $为一个有限的原始排列组，在$ω$上，具有非平凡点稳定器$g_α$。我们说，如果$g_α$以$ω\ setminus \ {α\} $为原始的每个轨道，则$ g $是极其原始的。在较早的工作中，曼恩，普拉格和血清已经证明，每个极端原始的群体几乎都是简单的，要么是仿射类型，而且他们已经将仿射组分类为最多有限的许多例外。最近，已经完全确定了几乎简单的极端原始群体。如果人们对几乎简单组的最大亚组数量进行了构想，那么Mann等人的结果。表明这只是消除仿射组的明确列表，以完成极端原始组的分类。 Mann等。猜想这些仿射候选者都不是极为原始的，我们的主要结果证实了这一猜想。
Let $G$ be a finite primitive permutation group on a set $Ω$ with nontrivial point stabilizer $G_α$. We say that $G$ is extremely primitive if $G_α$ acts primitively on each of its orbits in $Ω\setminus \{α\}$. In earlier work, Mann, Praeger and Seress have proved that every extremely primitive group is either almost simple or of affine type and they have classified the affine groups up to the possibility of at most finitely many exceptions. More recently, the almost simple extremely primitive groups have been completely determined. If one assumes Wall's conjecture on the number of maximal subgroups of almost simple groups, then the results of Mann et al. show that it just remains to eliminate an explicit list of affine groups in order to complete the classification of the extremely primitive groups. Mann et al. have conjectured that none of these affine candidates are extremely primitive and our main result confirms this conjecture.
