  A sharply 2-transitive permutation group of characteristic 0 whose point
stabiliser has an abelian subgroup of finite index splits. More generally, a
near-domain of characteristic 0 with a multiplicative subgroup of finite index
avoiding all multipliers $d_{a,b}$ must be a near-field. In particular this
answers question 12.48 b) of the Kourovka Notebook in characteristic 0.
