A bound for the class of certain nilpotent groups

The groups whose 2-generator subgroups are all nilpotent of class at most 2 are nilpotent of class at most 3 (see Levi [6]). Heineken [3] generalized Levi's result by proving that for n ≧ 3, if the n-generator subgroups of a group are all nilpotent of class at most n, then the group itself is nilpotent of class at most n. Other related problems have been considered by Bruck [1].