On the existence of complements in a group to some abelian normal subgroups - Dixon, M.R.; Kurdachenko, L.A.; Javier Otal (Algebra and Discrete Mathematics, 2010)
A complement to a proper normal subgroup H of a group G is a subgroup K such that G=HK and H∩K=⟨1⟩. Equivalently it is said that G splits over H. In this paper we develop a theory that we call hierarchy of centralizers to obtain sufficient conditions for a group to split over a certain abelian subgroup. We apply these results to obtain an entire group-theoretical wide extension of an important result due to D. J. S. Robinson formerly shown by cohomological methods.