A group $G$ is called a group with boundedly finite conjugacy classes (or a BFC-group) if $G$ is finite-by-abelian. A group $G$ satisfies the maximal condition on non-BFC-subgroups if every ascending chain of non-BFC-subgroups terminates in finitely many steps. In this paper the authors obtain the structure of finitely generated soluble-by-finite groups with the maximal condition on non-BFC subgroups.
AMS 2000 Mathematics subject classification: Primary 20E15. Secondary 20F16; 20F24