The linear instability of a rotating conducting liquid cylinder heated from below in a horizontal magnetic field is considered numerically. A condition for the magnetic suppression of the bulk rotation is obtained. If the bulk is rotation dominated then the linear instability is slightly delayed by the field and sets in as a rotating wave. If the bulk is dominated by the magnetic field then the instability has the form of field aligned convection rolls. Outside thin boundary layers the instability then becomes increasingly similar to the onset in a plain channel. The results are discussed in light of previous silicon growth experiments and existing knowledge from related problems. (C) 2012 Elsevier B.V. All rights reserved.