Diameter Bound for Finite Simple Groups of Large Rank

Abstract

Given a non-abelian finite simple group $G$ of Lie type, and an arbitrary generating set $S$, it is conjectured by Laszlo Babai that its Cayley graph $\Gamma (G,S)$ will have a diameter of $(\log |G|{)}^{O(1)}$. However, little progress has been made when the rank of $G$ is large. In this article, we shall show that if $G$ has rank $n$, and its base field has order $q$, then the diameter of $\Gamma (G,S)$ would be $q^{O(n(\log n+\log q{)}^3)}$.

arXiv commentReferee's comments incorporated

Cited by in corpus (2)

• Babai's conjecture for high-rank classical groups with random generators
• An improved diameter bound for finite simple groups of Lie type