The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups

Download or read book The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 2004 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small. A number of consequences are obtained. It follows from the main theorem that a simple algebraic group over an algebraically closed field has only finitely many conjugacy classes of maximal subgroups of positive dimension. It also follows that the maximal subgroups of sufficiently large order in finite exceptional groups of Lie type are known.