The Classification of the Finite Simple Groups, Number 9

Download or read book The Classification of the Finite Simple Groups, Number 9 written by Inna Capdeboscq and published by American Mathematical Society. This book was released on 2021-02-22 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the ninth volume in a series whose goal is to furnish a careful and largely self-contained proof of the classification theorem for the finite simple groups. Having completed the classification of the simple groups of odd type as well as the classification of the simple groups of generic even type (modulo uniqueness theorems to appear later), the current volume begins the classification of the finite simple groups of special even type. The principal result of this volume is a classification of the groups of bicharacteristic type, i.e., of both even type and of $p$-type for a suitable odd prime $p$. It is here that the largest sporadic groups emerge, namely the Monster, the Baby Monster, the largest Conway group, and the three Fischer groups, along with six finite groups of Lie type over small fields, several of which play a major role as subgroups or sections of these sporadic groups.