论文标题
$ sl（n，p）$的Cayley图的直径，带有包含转子的生成集
Diameter of Cayley graphs of $SL(n,p)$ with generating sets containing a transvection
论文作者
论文摘要
Babai的一个众所周知的猜想指出，如果$ g $是有限的简单组，而$ x $是$ g $的生成集，那么Cayley Graph $ cay（g，x）$的直径在上面由$（\ log | g |）^c $用于某些绝对常数$ c $。本文的目的是证明每当$ g = sl（n，p）$和$ x $的$ cay（g，x）$的直径是限制的。对于$ g = sl（n，k）$，也证明了这种结果的自然类似物，其中$ k $可以是任何字段。
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.
