Groups with an FC-nilpotent triple factorization (Q1120005)

The authors study groups G which have a triple factorization \(G=AB=AK=BK\) where A and B are subgroups, and K is a normal subgroup of G. Triple factorizations are important in the study of groups that are expressed as the product of a pair of subgroups. Let G be a group with a triple factorization \(G=AB=AK=BK\) in which K is a minimax group. Theorem: If A and B are FC-nilpotent, then so is G. Here ``FC-nilpotent'' can be replaced by ``FC-hypercentral'' and ``locally FC-nilpotent''. A similar result is proved for the case where G has finite abelian section rank and no hypothesis is placed on K.