central height; linear group; stability group
We compute the central heights of the full stability groups $S$ of ascending series and of descending series of subspaces in vector spaces over fields and division rings. The aim is to develop at least partial right analogues of results on left Engel elements and related nilpotent radicals in such $S$ proved recently by Casolo \& Puglisi, by Traustason and by the current author. Perhaps surprisingly, while there is an absolute bound on these central heights for descending series, for ascending series the central height can be any ordinal number.
 Robinson, D. J. S.: Finiteness Conditions and Generalized Soluble Groups. Part 1
. Springer Berlin (1972). MR 0332989
 Robinson, D. J. S.: Finiteness Conditions and Generalized Soluble Groups. Part 2
. Springer Berlin (1972). MR 0332990