有界李秩单群的积置换图的连通性
Connectivity of the Product Replacement Graph of Simple Groups of Bounded Lie Rank
摘要：
乘积替换算法是产生有限群的随机元的一种实用算法。该算法可以被描述为一个图上的随机游动，该图的顶点是该组的生成k元组（对于一个固定的整数k）。证明了存在一个函数c（r），使得对任意李秩为r的有限李型单群，其生成k-元组的乘积置换图对任意k > c（r）是连通的.证明使用的结果拉森和粉红色，不依赖于有限的单群的分类。
英文摘要：
The Product Replacement Algorithm is a practical algorithm for generating random elements of a finite group. The algorithm can be described as a random walk on a graph whose vertices are the generating k-tuples of the group (for a fixed integer k). We show that there is a function c(r) such that for any finite simple group of Lie type, with Lie rank r, the product replacement graph of the generating k-tuples is connected for any k > c(r). The proof uses results of Larsen and Pink and does not rely on the classification of finite simple groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
