Let G be a torsion-free abelian group and n be a (finite) cardinal. The group G is called n-QE-transitive if for any pure subgroups X; Y of rank n of G, there exists some endomorphism ' of G such that '.X / Â Y and Y ='.X/ is a torsion abelian group. We investigate these groups and obtain results similar to the ones for E-transitive groups.