论文标题
大型完全对称套件
Large totally symmetric sets
论文作者
论文摘要
完全对称的集合是一个组的子集，使得该子集的每个排列可以通过组中的共轭来实现。大型完全对称集的（非）存在阻碍了同构，因此特别使用了完全对称集的大小的界限。在本文中，我们证明，如果一个组具有完全对称的尺寸$ K $，则必须至少有$ $（k+1）！$。我们还表明，除三个例外，$ \ {（1 \; i）\ mid i = 2，\ ldots，n \} \ subset s_n $是唯一一个完全对称的集合，从而使此界尖锐；因此，它是相对于环境组大小的最大完全对称集。
A totally symmetric set is a subset of a group such that every permutation of the subset can be realized by conjugation in the group. The (non-)existence of large totally symmetric sets obstruct homomorphisms, so bounds on the sizes of totally symmetric sets are of particular use. In this paper, we prove that if a group has a totally symmetric set of size $k$, it must have order at least $(k+1)!$. We also show that with three exceptions, $\{(1 \; i)\mid i = 2,\ldots,n\} \subset S_n$ is the only totally symmetric set making this bound sharp; it is thus the largest totally symmetric set relative to the size of the ambient group.
