论文标题
在最小程度上的传递置换组中，稳定器是$ 2 $ - 组
On minimal degree of transitive permutation groups with stabiliser being a $2$-group
论文作者
论文摘要
排列组$ g $的最小程度定义为$ g $的非平凡元素的非固定点的最小数量。在本文中，我们表明，如果$ g $是一个及时的$ n $的瞬态排列组，没有非平凡的普通$ 2 $ 2 $ - 群体，使得稳定器是$ 2 $ - 组，那么$ g $的最低度为$ g $，至少为$ $ \ frac {2} {2} {3} n $。证明取决于有限简单组的分类。
The minimal degree of a permutation group $G$ is defined as the minimal number of non-fixed points of a non-trivial element of $G$. In this paper we show that if $G$ is a transitive permutation group of degree $n$ having no non-trivial normal $2$-subgroups such that the stabiliser of a point is a $2$-group, then the minimal degree of $G$ is at least $\frac{2}{3}n$. The proof depends on the classification of finite simple groups.
