The transitive groups of degree 48 and some applications
The transitive groups of degree 48 and some applications
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DOI：
10.1016/j.jalgebra.2021.06.018
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发表时间：
2021-02
影响因子：
0.9
通讯作者：
D. Holt;G. Royle;Gareth Tracey
中科院分区：
文献类型：
--
作者：
D. Holt;G. Royle;Gareth Tracey
本文的主要目的是报告在岩浆的成功计数的代表195 826 352共轭类的传递子群的对称群S48的度48。此外，我们已经确定，25707这些群体是最小的传递，其中713是难以捉摸的。最小传递的例子已被用来枚举的点传递群的度为48，其中有1 538 868 366，其中所有的，但0.1625%的凯莱图。我们还发现，生成这些群所需的元素的最大数量是10，我们利用这一事实来改进第三作者以前关于生成给定度的任意传递置换群所需元素数量的一般界限。这个改进的界限的证明的细节将作为单独的文件发表。
The primary purpose of this paper is to report on the successful enumeration in Magma of representatives of the 195 826 352 conjugacy classes of transitive subgroups of the symmetric group S 48 of degree 48. In addition, we have determined that 25707 of these groups are minimal transitive and that 713 of them are elusive. The minimal transitive examples have been used to enumerate the vertex-transitive groups of degree 48, of which there are 1 538 868 366, all but 0.1625% of which arise as Cayley graphs. We have also found that the largest number of elements required to generate any of these groups is 10, and we have used this fact to improve previous general bounds of the third author on the number of elements required to generate an arbitrary transitive permutation group of a given degree. The details of the proof of this improved bound will be published as a separate paper.