Around 1980, G Mason announced the classification of a certain subclass of a class of finite simple groups known as 'quasithin groups'. The classification of the finite simple groups depends upon a proof that there are no unexpected groups in this subclass

Around 1980, G. Mason announced the classification of a certain subclass of an important class of finite simple groups known as quasithin groups. The classification of the finite simple groups depends upon a proof that there are no unexpected groups in this subclass. Unfortunately Mason neither completed nor published his work. In the Main Theorem of this two-part book (Volumes 111 and 112 in the AMS series, Mathematical Surveys and Monographs) the authors provide a proof of a stronger theorem classifying a larger class of groups, which is independent of Mason's arguments. In particular, this...