A nonlinear maximal group topology

We show that, assuming Martinʼs Axiom MA, there is a nonlinear maximal group topology. That is, assuming MA, there is an ultrafilter U on ⊕ωZ2 such that the filter N={A∪{0}:A∈U} has no base consisting of subgroups, but for every U∈N, there is V∈N such that V+V⊆U.