GALOIS COHOMOLOGY OF SPECIAL ORTHOGONAL GROUPS

If (A, sigma) is a central simple algebra of even degree with orthogon al involution, then for the map of Galois cohomology sets from H-1(F, SO(A, sigma)) to the 2-torsion in the Brauer group of F, we describe f ully the image of a given element of H-1(F, SO(A, sigma)) and prove th at this description is correct in two different ways. As an easy conse quence, we derive a result of Bartels [Bar, Satz 3].