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arXiv · 2002.10443

Diameter of Cayley graphs of $SL(n,p)$ with generating sets containing a transvection

Zoltán Halasi
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Abstract

A well-known conjecture of Babai states that if $G$ is a finite simple group and $X$ is a generating set of $G$, then the diameter of the Cayley graph $Cay(G,X)$ is bounded above by $(\log |G|)^c$ for some absolute constant $c$. The goal of this paper is to prove such a bound for the diameter of $Cay(G,X)$ whenever $G=SL(n,p)$ and $X$ is a generating set of $G$ which contains a transvection. A natural analogue of this result is also proved for $G=SL(n,K)$, where $K$ can be any field.

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Zoltán Halasi. 2020-02-24. Diameter of Cayley graphs of $SL(n,p)$ with generating sets containing a transvection. https://arxiv.org/abs/2002.10443

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