FC-NILPOTENT PRODUCTS OF HYPERCENTRAL GROUPS

It is shown that an FC-nilpotent group G = AB = AK = BK which is the p roduct of two hypercentral subgroups A and B and a nilpotent normal su bgroup K of G is hypercentral. This implies that if the FC-nilpotent g roup G = AB is the product of a proper nilpotent subgroup A and a prop er hypercentral subgroup B then A or B is contained in a proper normal subgroup of G.