Moufang sets from groups of mixed type

Abstract

We consider the existence of Moufang sets related to certain groups of mixed type. This way, we obtain new examples of Moufang sets and new constructions of known classes. The most interesting class of new examples is related to the Moufang quadrangles of type F 4 and to the Ree–Tits octagon over a nonperfect field, and the root groups of each member have nilpotency class three.