منابع مشابه
Growth in Finite Simple Groups of Lie Type
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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The beautiful book of Terry Tao starts with the following words: Expander graphs are a remarkable type of graph (or more precisely, a family of graphs) on finite sets of vertices that manage to simultaneously be both sparse (low-degree) and “highly connected” at the same time. They enjoy very strong mixing properties: if one starts at a fixed vertex of an (two-sided) expander graph and randomly...
متن کاملFinite 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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In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.
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We give bounds on the shortest identity in finite simple groups of Lie type.
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2014
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-2014-00821-3