论文标题
几乎难以捉摸的排列组
Almost elusive permutation groups
论文作者
论文摘要
令$ g $为有限套件$ω$上的非平凡及其及其置换组。如果$ g $的元素在$ω$上没有固定点，则据说是一种危险。从轨道计数引理中，$ g $包含一个杂物，实际上，$ g $包含Fein，Kantor和Schacher定理的质量命令的危险。但是，有一些没有主要秩序危险的团体。这些是所谓的难以捉摸的群体，近年来它们已经得到了广泛的研究。扩展了这个概念，我们说$ g $几乎难以捉摸，如果它包含了主要命令的奇异性类别。在本文中，我们首先证明了每个准灵感几乎难以捉摸的群体几乎是简单的，要么是$ 2 $的仿射类型。然后，我们将几乎简单且原始的所有几乎难以捉摸的群体与Socle交替组，零星组或一组谎言类型进行分类。
Let $G$ be a nontrivial transitive permutation group on a finite set $Ω$. An element of $G$ is said to be a derangement if it has no fixed points on $Ω$. From the orbit counting lemma, it follows that $G$ contains a derangement, and in fact $G$ contains a derangement of prime power order by a theorem of Fein, Kantor and Schacher. However, there are groups with no derangements of prime order; these are the so-called elusive groups and they have been widely studied in recent years. Extending this notion, we say that $G$ is almost elusive if it contains a unique conjugacy class of derangements of prime order. In this paper we first prove that every quasiprimitive almost elusive group is either almost simple or $2$-transitive of affine type. We then classify all the almost elusive groups that are almost simple and primitive with socle an alternating group, a sporadic group, or a rank one group of Lie type.
