A Further Generalization of the Glauberman-Thompson p-Nilpotency Criterion in Fusion Systems

Let [Formula: see text] be a prime and [Formula: see text] be a fusion system over a finite [Formula: see text]-group [Formula: see text]. The fusion system [Formula: see text] is said to be nilpotent if [Formula: see text]. Using [Formula: see text]-strongly closed subgroups, we provide a new criterion for a saturated fusion system [Formula: see text] to be nilpotent, which may be viewed as extending the Glauberman-Thompson [Formula: see text]-nilpotency criterion to fusion systems.