A NOTE ON GEOMETRIC FACTORIALITY

Let k be a perfect field such that (k) over bar is solvable over k. We show that a smooth, affine, factorial surface birationally dominated by affine 2-space A(k)(2) is geometrically factorial and hence isomorphic to A(k)(2). The result is useful in the study of subalgebras of polynomial algebras. The condition of solvability would be unnecessary if a question we pose on integral representations of finite groups has a positive answer.