论文标题
Babai对高级古典群体的猜想与随机发电机
Babai's conjecture for high-rank classical groups with random generators
论文作者
论文摘要
令$ g = \ mathrm {scl} _n（q）$是一个Quasisimple古典群，带有$ n $大，然后$ x_1，\ dots，x_k \ in G $ andom，其中$ k \ geq q^c $。我们表明，由此产生的Cayley图的直径由$ q^2 n^{o（1）} $带有概率$ 1 -o（1）$的界限。在特定情况下，$ g = \ mathrm {sl} _n（p）$带有$ p $ a的大小的素数，我们表明，$ k = 3 $相同。
Let $G = \mathrm{SCl}_n(q)$ be a quasisimple classical group with $n$ large, and let $x_1, \dots, x_k \in G$ random, where $k \geq q^C$. We show that the diameter of the resulting Cayley graph is bounded by $q^2 n^{O(1)}$ with probability $1 - o(1)$. In the particular case $G = \mathrm{SL}_n(p)$ with $p$ a prime of bounded size, we show that the same holds for $k = 3$.
