On the exponent of a certain quotient of Whitehead groups of division algebras.

Let D be an F-central division algebra. In this paper, we investigated the exponent of the group G (D) = D * / Nrd D (D *) D ′ , where D * is the group of units of D, Nrd D (D *) is the image of D * under the reduced norm map and D ′ is the commutator subgroup of D * . We show that if exp (G (D)) < ind (D) , then D and F satisfy strong conditions. In particular, we observe that if D is a sum cyclic algebras in Br (F) , then exp (G (D)) < ind (D) if and only if F is euclidean and D is a tensor product of an ordinary quaternion algebra and a division algebra of odd index. [ABSTRACT FROM AUTHOR]