Trifactorized locally finite groups with min-p for every prime p

A group G is trifactorized if G = AB = AC = BC with three subgroups A, B and C of G. Some structural theorems about trifactorized locally finite groups with minimum condition on p-subgroups for every prime p are proved. For instance, it is shown that G is locally supersoluble (locally nilpotent) if A and B are locally nilpotent and C is locally supersoluble (locally nilpotent). The second and the third author wish to thank the Institute of Mathematics of the University of Mainz for their excellent hospitality during the preparation of this paper. The second author is grateful to the University of Stellenbosch, South Africa, and the third author to the Deutsche Forschungsgemeinschaft (DFG) for financial assistance.