The Ring of Invariants of O(3, q)

Letp be an odd prime integer and qbe the Galois field withq=pνelements. Let , which is a nondegenerate quadratic form, and denote by O(3, q) the corresponding orthogonal group. The purpose of this note is to give a new proof of a theorem of S. D. Cohen on the structure of q[x, y, z]O(3, q). The novelty of our proof lies in the description of the generators in terms of the geometry of ovals in q (2) and Steenrod operations.