A necessary and sufficient condition for a group to be the multiplicative group of a field (Q1061233)

The problem of describing those abelian groups which can be multiplicative groups of fields has been solved by \textit{R. M. Dicker} [Proc. Lond. Math. Soc., III. Ser. 18, 114-124 (1968; Zbl 0191.325)] in terms of a certain function on the group. In this paper the author gives another necessary and sufficient condition for a group in terms of the existence of a certain extension of the group. The results depend heavily on those of Dicker.