Finite simple groups of Lie type as expanders

Lubotzky, Alexander. "Finite simple groups of Lie type as expanders." Journal of the European Mathematical Society 013.5 (2011): 1331-1341. <http://eudml.org/doc/277517>.

@article{Lubotzky2011,
abstract = {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 $\{SL\}_2$ which is obtained by combining results of Selberg and Drinfeld via an explicit construction of Ramanujan graphs by Lubotzky, Samuels and Vishne.},
author = {Lubotzky, Alexander},
journal = {Journal of the European Mathematical Society},
keywords = {finite simple groups of Lie type; non-Abelian finite simple groups; projective special linear groups; generators; Cayley graphs; uniform expanders; finite simple groups of Lie type; non-Abelian finite simple groups; projective special linear groups; generators; Cayley graphs; uniform expanders},
language = {eng},
number = {5},
pages = {1331-1341},
publisher = {European Mathematical Society Publishing House},
title = {Finite simple groups of Lie type as expanders},
url = {http://eudml.org/doc/277517},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Lubotzky, Alexander
TI - Finite simple groups of Lie type as expanders
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 5
SP - 1331
EP - 1341
AB - 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 ${SL}_2$ which is obtained by combining results of Selberg and Drinfeld via an explicit construction of Ramanujan graphs by Lubotzky, Samuels and Vishne.
LA - eng
KW - finite simple groups of Lie type; non-Abelian finite simple groups; projective special linear groups; generators; Cayley graphs; uniform expanders; finite simple groups of Lie type; non-Abelian finite simple groups; projective special linear groups; generators; Cayley graphs; uniform expanders
UR - http://eudml.org/doc/277517
ER -