ON THE PROJECTIVE SCHUR GROUP OF A FIELD

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 grou p algebra k(alpha)G with G finite, alpha is an element of H-2(G, k). It has been conjectured by Nelis and Van Oystaeyen (J. Algebra 137 (19 91), 501-518) that PS(k) = Br(k) for all fields k. We disprove this co njecture by showing that PS(k) not equal Br(k) for rational function f ields k(0)(x) where k(0) is any infinite field which is finitely gener ated over its prime field. (C) 1995 Academic Press. Inc.