Normal subgroups of groups which are products of two Abelian subgroups

Abstract

It is shown that if a group G = A B G = AB , where A A and B B are Abelian subgroups of G , A ≠ B G,A \ne B , and either A A or B B satisfies the maximum condition, then there is a normal subgroup N N of G G , N ≠ G N \ne G , such that N N contains either A A or B B .