论文标题
在经典组的Cayley图的直径上，具有包含TransTrive的生成集
On the diameter of Cayley graphs of classical groups 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 $是任何有限的简单组，而$ x $是$ g $的生成集，那么Cayley Graph $ cay（G，x）$的直径由$ \ log | g |^c $界定，用于某些通用常数$ c $。在本文中，我们证明了$ cay（g，x）$ for $ g = psl（n，q），psp（n，q）$或$ psu（n，q）$的限制，其中$ q $是奇怪的，在假设$ x $包含Transvection和$ q \ neq 9 $或$ 81 $的情况下。
A well-known conjecture of Babai states that if $G$ is any finite simple group and $X$ is a generating set for $G$, then the diameter of the Cayley graph $Cay(G,X)$ is bounded by $\log|G|^c$ for some universal constant $c$. In this paper, we prove such a bound for $Cay(G,X)$ for $G=PSL(n,q),PSp(n,q)$ or $PSU(n,q)$ where $q$ is odd, under the assumptions that $X$ contains a transvection and $q\neq 9$ or $81$.
