On the Projective Schur Group of a Field Original Research Article

If k is a field, the projective Schur group PS(k) of k is the subgroup of the Brauer group Br(k) consisting of those classes which contain a projective Schur algebra, i.e., a homomorphic image of a twisted group algebra kαG with G finite, α set membership, variant H2(G, k*). It has been conjectured by Nelis and Van Oystaeyen (J. Algebra137 (1991), 501-518) that PS(k) = Br(k) for all fields k. We disprove this conjecture by showing that PS(k) ≠ Br(k) for rational function fields k0(x) where k0 is any infinite field which is finitely generated over its prime field.