ON THE 1-COHOMOLOGY OF FINITE GROUPS OF LIE TYPE

Publisher Summary This chapter discusses the problem of calculating H1(Gσ,V) where G is a finite group of Lie type over K = GF(q) and V is a minimal G -module. It discusses two methods used for determining upper bounds on dim H1 (Gσ,V(λ)). The first method assumes r > 3, and is applicable to nonminimal modules (and can in fact be used to obtain the vanishing of H1 (Gσ,V) in many instances). The second method is an inductive procedure that does not depend on the size of the field but depends heavily on the minimality of V (λ). The second method has only been tried for the split Chevalley groups.