Element orders in covers of finite simple groups of Lie type
نویسندگان
چکیده
منابع مشابه
Black-box recognition of finite simple groups of Lie type by statistics of element orders
Given a black-box group G isomorphic to some finite simple group of Lie type and the characteristic of G, we compute the standard name of G by a Monte Carlo algorithm. The running time is polynomial in the input length and in the time requirement for the group operations in G. The algorithm chooses a relatively small number of (nearly) uniformly distributed random elements of G, and examines th...
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Given a matrix group G = 〈X〉 GL(d,q), specified by a set X of generators, it seems that a full structural exploration of G is necessary in order to answer even the simplest questions concerning G , such as finding |G| or testing the membership of any given matrix in G (cf. [LG,BB]). Currently, the standard approach to such an exploration is to set up a recursive scheme of homomorphisms, breakin...
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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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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...
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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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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2015
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498815500565