Finite simple groups of Lie type as expanders

• Autores: Alexander Lubotzky
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 13, Nº 5, 2011, págs. 1331-1341
• Idioma: inglés
• DOI: 10.4171/jems/282
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• Resumen

  • We prove that all finite simple groups of Lie type, with the exception of the Suzuki groups, can be made into a family of expanders in a uniform way. This confirms a conjecture of Babai, Kantor and Lubotzky from 1989, which has already been proved by Kassabov for sufficiently large rank. The bounded rank case is deduced here from a uniform result for SL2 which is obtained by combining results of Selberg and Drinfeld via an explicit construction of Ramanujan graphs by Lubotzky, Samuels and Vishne.