Groups with finiteness conditions on the lower central series of non-normal subgroups

It is known that any locally graded group with finitely many derived subgroups of non-normal subgroups is finite-by-abelian. This result is generalized here, by proving that in a locally graded group G the subgroup gamma(k)(G) is finite if the set {gamma(k)(H) | H <= G, H (sic) G} is finite. Moreover, locally graded groups with finitely many kth terms of lower central series of infinite non-normal subgroups are also completely described.