Construction of Curtis-Phan-Tits system in black box classical groups.

link: http://arxiv.org/abs/1008.2823
Abstract

We present a polynomial time Monte-Carlo algorithm for finite simple black
box classical groups of odd characteristic which constructs all root
${\rm{SL}}_2(q)$-subgroups associated with the nodes of the extended Dynkin
diagram of the corresponding algebraic group.