The author presents - without proofs - a series of results on finite groups G having subgroups A and B such that \(G=AB\) or \(G=ABA\). Amongst other things he obtains some non-simplicity criteria and characterizations of certain simple groups. Applying his techniques to infinite periodic groups he gets the following theorem: Let \(G=AB\) be a locally finite group, where A and B are nilpotent groups with finite commutator subgroups. Then G is solvable.