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On the maximal number of elements pairwise generating the finite alternating group
Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2024-02-14 , DOI: 10.1016/j.jcta.2024.105870
Francesco Fumagalli , Martino Garonzi , Pietro Gheri

Let be the alternating group of degree . Let be the maximal size of a subset of such that whenever and and let be the minimal size of a family of proper subgroups of whose union is . We prove that, when varies in the family of composite numbers, tends to 1 as . Moreover, we explicitly calculate for congruent to 3 modulo 18.

中文翻译:

关于成对生成有限交替群的最大元素数

让 是 度 的交替群。设 为 的子集的最大大小,每当 且 为 并集为 的真子群族的最小大小。我们证明,当合数族发生变化时,趋向于 1。此外,我们明确计算 3 模 18 同余。
更新日期:2024-02-14
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