论文标题
通用线性组中的完全对称集
Totally symmetric sets in the general linear group
论文作者
论文摘要
一个完全对称的集合是一个组的有限子集，在环境组中，可以通过共轭来实现元素的任何排列。这种集合在同态下是刚性的，因此对代数结构产生了很大的控制。在本文中，我们介绍了对总对称性的更一般的观点，并为通用线性群中完全对称集的“不可约性”概念提出了概念。我们对不可检查的完全对称集和最大基数分类。
A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the algebraic structure. In this paper we introduce a more general perspective on total symmetry, and formulate a notion of "irreducibility" for totally symmetric sets in the general linear group. We classify irreducible totally symmetric sets, as well as those of maximal cardinality.
