On 2-Symmetric Words in Nilpotent Groups - Gupta, S.; Holubowski, W. (Ukrains’kyi Matematychnyi Zhurnal, 2002)
We find the nilpotency class of a group of 2-symmetric words for free nilpotent groups, free nilpotent metabelian groups, and free (nilpotent of class c)-by-Abelian groups.