A note on a result of Skiba

Let H be a subgroup of a group G. In this paper, we say that H is E-supplemented in G if there is a subgroup K of G such that G = HK and H boolean AND K <= H-eG, where H-eG denotes the subgroup of H generated by all those subgroups of H which are S-quasinormally embedded in G. We strengthen a nice result of Skiba which gives a positive answer to an open question of Shemetkov.