Classical groups, probabilistic methods, and the (2,3)-generation problem

• 成果类型: Article
• 署名作者: Liebeck, MW; Shalev, A
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/2118584
• 发表日期: 1996
• 页码: 77-125
• 关键词: finite chevalley-groups; maximal-subgroups; generation

摘要

We study the probability that randomly chosen elements of prescribed type in a finite simple classical group G generate G; in particular, we prove a conjecture of Kantor and Lubotzky in this area. The probabilistic approach is then used to determine the finite simple classical quotients of the modular group PSL(2)(Z), up to finitely many exceptions.