Finite Groups of Uniform Logarithmic Diameter
Miklós Abért, László Babai · arXiv (Cornell University) · 2005
We give an example of an infinite family of finite groups $G_n$ such that each $G_n$ can be generated by 2 elements and the diameter of every Cayley graph of $G_n$ is $O(\log (| G_{n}|))$. This answers a question of Lubotzky.