Full description of stable elements of free nilpotent group F2, 12

This paper deals with the search for stable elements with inhomogeneous appearance of generators in free nilpotent groups of rank two and stage 12. The automorphic images of commutators with inhomogeneous appearance of generators are studied. We proved the theorem about non exist stable elements among nontrivial linear combinations of such elements. We considered the case of construction of stable element, consisting of the basic commutators with homogeneous and inhomogeneous appearance of generators.