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 stabilizer of a point is a 2-group, then the minimal degree of G is at least 23⁢n{\frac{2}{3}n}. The proof depends on the classification of finite simple groups.

中文翻译：

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关于带有稳定子的传递性置换群的最小程度，一个2-群

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n个阶的传递性置换群，且没有非平凡的正常2个子群，使得一个点的稳定子为2个群，则G的最小阶至少为23⁢ n {\ frac {2} {3} n}。证明取决于有限简单组的分类。