Babai's conjecture for high-rank classical groups with random generators

• 成果类型: Article
• 署名作者: Eberhard, Sean; Jezernik, Urban
• 署名单位: University of Cambridge; University of Ljubljana
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01065-x
• 发表日期: 2022
• 页码: 149-210
• 关键词: finite simple-groups; sharp bounds; diameter; probability; GROWTH

摘要

Let G = SCln(q) be a quasisimple classical group with n large, and let x(1),..., x(k) is an element of G be random, where k >= q(C). We show that the diameter of the resulting Cayley graph is bounded by q(2)n(O(1)) with probability 1 - o(1). In the particular case G = SLn(p) with p a prime of bounded size, we show that the same holds for k = 3.