Criteria for nilpotency of fusion systems

Let p be an odd prime and let F be a fusion system over a finite p-group P. A fusion system F is said to be nilpotent if F=FP(P). In this paper we provide new criteria for saturated fusion systems F to be nilpotent, which can be viewed as extension of the p-nilpotency theorem of Glauberman and Thompson for fusion systems attributed to Kessar and Linckelmann.