CHARACTERIZING THE MULTIPLICATIVE GROUPOF A REAL CLOSED FIELD IN TERMS OF ITSDIVISIBLE MAXIMAL SUBGROUP

Let F be a field and , 1 be a maximal subgroup of themultiplicative group F = F {O} of index p. It is proved that if M is divisible. then Br.( F) P ≠ 0 if and only if p = 2 and F is Euclidean, Furthermore, it is shown that in this case F* contains a divisible maximal subgroup if and only if F is is omorphic to the multiplicative group of a real closed field.