Finite simple groups of Lie type as expanders
نویسندگان
چکیده
منابع مشابه
Finite Simple Groups of Lie Type as Expanders
are uniform expanders. Nikolov [N] proved that every classical group is a bounded product of SLn(q)’s (with possible n = 2, but the proof shows that if the Lie rank is sufficiently high, say ≥ 14, one can use SLn(q) with n ≥ 3). Bounded product of expander groups are uniform expanders. Thus together, their results cover all classical groups of high rank. So, our Theorem is new for classical gro...
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We prove that if L is a finite simple group of Lie type and A a symmetric set of generators of L, then A grows i.e |AAA| > |A| where ε depends only on the Lie rank of L, or AAA = L. This implies that for a family of simple groups L of Lie type of bounded rank the diameter of any Cayley graph is polylogarithmic in |L|. Combining our result on growth with known results of Bourgain, Gamburd and Va...
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ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2011
ISSN: 1435-9855
DOI: 10.4171/jems/282