Finite simple groups which projectively embed in an exceptional Lie group 
are classified!
Bull. Amer. Math. Soc. 36 (1999), pp. 75-93 
Robert L. Griess Jr.
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1003  
and A. J. E. Ryba
Department of Mathematics, Marquette University, Milwaukee, WI 53201-1881
Current address: Department of Mathematics, Queens College, CUNY, Flushing, 
NY 11367-1597  

Abstract. Since finite simple groups are the building blocks of finite groups, 
it is natural to ask about their occurrence ``in nature''. In this article, we 
consider their occurrence in algebraic groups and moreover discuss the general 
theory of finite subgroups of algebraic groups.