Saturated fusion systems on $p$-groups of maximal class

Abstract

For a prime number p, a finite p-group of order p n has maximal class if it has nilpotency class n − 1. Here we examine saturated fusion systems on maximal class p-groups and, in particular, we describe all the reduced saturated fusion systems on these groups.

Exotic Fusion Systems Related to Sporadic Simple Groups

“…The exotic fusion systems described in Theorem D and Theorem E are reminiscent of the exotic fusion systems supported on p-groups of maximal class, as determined in [GP20]. There, in almost all cases where F is an exotic fusion systems, there is a class of essential subgroups which are pearls: essential subgroups isomorphic to p 2 or p 1+2 + .…”