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arXiv · 1511.08535

Diameter Bound for Finite Simple Groups of Large Rank

Arindam Biswas·Yilong Yang
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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 $q^{O(n(\log n + \log q)^3)}$.

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Arindam Biswas, Yilong Yang. 2015-11-27. Diameter Bound for Finite Simple Groups of Large Rank. https://doi.org/10.1112/jlms.12018

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