Minoration de la hauteur de Weil dans un compositum de corps de rayon

The study of Property (B) starts as a special case of Lehmer’s conjecture. An algebraic field is said to satisfy Property (B) if there exists a positive constant bounding by below the height of every point of infinite order. In this paper we prove that, under certain uniformity conditions, the compositum of a familly of fields satisfies Property (B).