On Thompson’s p-complement theorems for saturated fusion systems

Abstract

In this short note we prove that a saturated fusion system admitting some special type of automorphism is nilpotent. This generalizes classical results by J.G. Thompson.

A cohomological characterization of nilpotent fusion systems

“…Already several authors have provided fusion system counterparts to characterizations of p-nilpotency for finite groups, see [2], [3], [7], [9], [10], [11], [13] and [14]. In this work, we prove the fusion system version of a p-nilpotency criterion from the late 60's due to Wong [16] and Hoechsmann, Roquette and Zassenhaus [12].…”