Soluble groups with many 2-generator torsion-by-nilpotent subgroups

Abstract

We prove in this paper that a finitely generated soluble group in which every infinite subset contains a pair of distinct elements x, y such that x, y is torsion-by-nilpotent (respectively, x, x y is Chernikov-by-nilpotent), is itself torsion-by-nilpotent (respectively, finite-by-nilpotent).