An improved diameter bound for finite simple groups of Lie type

Halasi, Zoltán and Maróti, Attila and Pyber, László and Qiao, Youming (2019) An improved diameter bound for finite simple groups of Lie type. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. ISSN 0024-6093

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Abstract

For a finite group G, let diam(G) denote the maximum diameter of a connected Cayley graph of G. A well-known conjecture of Babai states that diam(G) is bounded by (log2|G|)O(1) in case G is a non-abelian finite simple group. Let G be a finite simple group of Lie type of Lie rank n over the field Fq. Babai's conjecture has been verified in case n is bounded, but it is wide open in case n is unbounded. Recently, Biswas and Yang proved that diam(G) is bounded by qO(n(log2n+log2q)3). We show that in fact diam(G)

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