The Automorphisms of the Group of Rotations and its Projective Group Corresponding to Quadratic Forms of any Index

Abstract

Let M be a vector space of dimension n over a field K of characteristic ≠2 and f a non-degenerate quadratic form on M. The automorphisms of the orthogonal group On(K,f), the rotation group On+(K,f), and their corresponding projective groups POn(K,f), POn+(K,f), were determined by J. Dieudonné for n sufficiently large under the condition that the index of f is greater than zero (see 2).