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Let $p$ be a prime and $\mathcal{F}$ be a saturated fusion system over afinite $p$-group $P$. The fusion system $\mathcal{F}$ is said to be nilpotentif $\mathcal{F}=\mathcal{F}_{P}(P)$. We provide new criteria for a saturatedfusion system $\mathcal{F}$ to be nilpotent, which may be viewed as extendingthe Glauberman-Thompson $p$-nilpotency criterion to fusion systems.

A further generalization of the Glauberman-Thompson $p$-nilpotency criterion in fusion systems