Groups Satisfying the Double Chain Condition on Non-Abelian Subgroups

If [Formula: see text] is a subgroup property, a group [Formula: see text] is said to satisfy the double chain condition on [Formula: see text]-subgroups if it admits no infinite double sequences [Formula: see text] consisting of [Formula: see text]-subgroups. The structure of generalized radical groups satisfying the double chain condition on non-abelian subgroups is described.