Nilpotent fusion systems

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].…”

On finite p-groups of supersoluble type

“…It is clear that every nilpotent saturated fusion system in the sense of [11] is supersoluble and every supersoluble saturated fusion system is soluble in the sense of [1, Part II, Definition 12.1]. Definition 2.…”

Control of fusion by Abelian subgroups of the hyperfocal subgroup

“…A fusion system F on S is called nilpotent if F = F S (S). Restricting attention to subgroups of the hyperfocal subgroup is motivated by a theorem of the second author of this paper together with Zhang, which characterizes p-nilpotency of a saturated fusion system F by the fusion on certain subgroups of the hyperfocal subgroup of F ; see [14]. Another motivation comes from work of Ballester-Bolinches, Ezquerro, Su and Wang [2] showing that, in certain special cases, fusion is detected on the subgroups of the focal subgroup of F which are cyclic of order p or 4.…”