Stability groups of series in vector spaces

We study the relationships between the subsets of left and bounded left Engel elements and various canonical locally nilpotent subgroups, in particular the Hirsch–Plotkin radical and the Fitting subgroup, of the stability groups of series of subspaces in vector spaces over fields and division rings. In this we extend work of C. Casolo and O. Puglisi and of G. Traustason.