Allan Adler Automorphism Groups of Certain Hypersurfaces Ii

In this article, we determine the automorphism groups of a family of cubic hypersurfaces generalizing those introduced in part I. Along the way, we determine all algebraic groups which contain PSL2(Fq) and which lie in PGLn(C), where q = 2n ± 1. This is accomplished using the classification of finite simple groups, information from the ATLAS of finite simple groups, the degrees of some complex representations of reductive groups over a finite field and techniques from Part I of this article needed to prove that the automorphism groups in question are finite. (1985) AMS Classification Numbers : 14D25, 14L30, 14L35, 14L40, 20B25, 20C15, 20C20, 20C25, 20C30, 20C33, 20D05, 20D06, 20D08, 20D45, 20D50, , 22E28, 20E32, 20G20, 20G40