Divisible modulo its torsion group field

‎For some absolutely algebraic field $F_0$ of characteristic $p 0$ and‎ ‎$\kappa$ an infinite cardinal‎, ‎it is shown that there exists a‎ ‎field $F$ such that ‎ $F^*\cong F^*_0\oplus(\oplus_\kappa‎‎\mathbb{Q})$‎.