Products of Locally Supersoluble Groups

Abstract

A group G is said to be FC-hypercentral if every non-trivial homomorphic image of G contains some non-trivial element having only finitely many conjugates. It is proved that if the FC-hypercentral group G = AB = AC = BC is factorized by three locally supersoluble subgroups A,B and C, and the commutator subgroup of G is nilpotent, then G is locally supersoluble