Growth and generation in SL2(Z/p Z)

• Autores: Harald Andrés Helfgott
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 167, Nº 2, 2008, págs. 601-623
• Idioma: inglés
• DOI: 10.4007/annals.2008.167.601
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• Resumen

  • 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((log p)c) elements of A ? A-1, where c and the implied constant are absolute.