标题： 具有准半正则元素的有限置换群 显示英文标题

标题： Finite permutation groups with quasi-semiregular elements

摘要： 在置换群中，准半正则元素是一个具有唯一固定点并在其余点上半正则作用的元素。 此类元素最初是在图的自同构背景下进行研究的，并在许多置换群族中自然出现，例如弗罗贝尼乌斯群和扎森豪斯群。 它们也出现在具有强$p$-嵌入子群的群的背景下。 我们研究哪些有限置换群包含准半正则元素，特别关注本原置换群。 我们确定可以包含准半正则元素的本原群的 O'Nan-Scott 类型，并将问题简化为仿射和几乎单的情况。 在几乎单的情况下，当底数为交替群或散在群时，我们获得了完整的分类。 显示英文摘要

摘要： A quasi-semiregular element in a permutation group is an element that has a unique fixed point and acts semiregularly on the remaining points. Such elements were first studied in the context of automorphisms of graphs and occur naturally in many families of permutation groups, such as Frobenius and Zassenhaus groups. They also arise in the context of groups with a strongly $p$-embedded subgroup. We investigate the question of which finite permutation groups contain quasi-semiregular elements, with particular attention to the primitive permutation groups. We determine the O'Nan-Scott types of primitive groups that can contain quasi-semiregular elements and reduce the question to the affine and almost simple cases. In the almost simple case, we obtain a complete classification when the socle is alternating or sporadic.