Growth and generation in SL2(Z/pZ)

• 成果类型: Article
• 署名作者: Helfgott, H. A.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2008.167.601
• 发表日期: 2008
• 页码: 601-623
• 关键词: finite-groups; random-walk; bounds; diameter; THEOREM; FIELDS; graphs; sums

摘要

We show that every subset of SL2(Z/pZ) grows rapidly when it acts on itself by the group operation. It follows readily that, for every set of generators A of SL2(Z/pZ), every element of SL2(Z/pZ) can be expressed as a product of at most O((logp)(c)) elements of A boolean OR A(-1), where c and the implied constant are absolute.