abstract: The complement to an arrangement of central hyperplanes in the complex space fibers over C with Milnor fiber F whose homology is not known in general. The arrangement will be called "a-monodromic" if the geometric monodromy acts trivially on the first homology of the Milnor fiber. We consider the problem of determining the a-monodromicity of the arrangement, giving some conjecture, and using a group theoretical approach to solve it in some cases.