Right Engel elements of stability groups of general series in vector spaces

Let V be an arbitrary vector space over some division ring D, L a general series of subspaces of V covering all of V \ {0} and S the full stability subgroup of L in GL(V). We prove that always the set of bounded right Engel elements of S is equal to the w-th term of the upper central series of S and that the set of right Engel elements of S is frequently equal to the hypercentre of S.