R-Rank of the Groups of Exceptional Lie Type

摘要

A result settling a question raised at the end of Borel and Serre (1953) cf. Borel, 1983 pp. 228 and 708 is proved. Let r be a prime and G a simple algebraic group of exceptional type over an algebraically closed field of characteristic not=r. Let E be an elementary abelian r-subgroup of G of maximal rank. Then rank(E)=Lie rank(G) with the exception of r=2 and G=G2, F4, the adjoint E7, and E8, in which cases rank(E)=lie rank(G)+1. Moreover, E is unique up to conjugacy.