  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 $\{\gamma_{k}(H)\;|\;H\ntriangleleft G\}$
is finite. Moreover, locally graded groups with finitely many $k$th terms of
lower central series of infinite non-normal subgroups are also completely
described.
