On the second-largest Sylow subgroup of a finite simple group of Lie type

S. P. Glasby, Alice C. Niemeyer, Tomasz Popiel

Let $T$ be a finite simple group of Lie type in characteristic $p$, and let $S$ be a Sylow subgroup of $T$ with maximal order. It is well known that $S$ is a Sylow $p$-subgroup exc…