Hirsch–Plotkin radical of stability groups

We study the Hirsch–Plotkin radical of stability groups of (general) subspace series of infinite dimensional vector spaces. We show that in countable dimension and some other cases, the HP-radical of the stability group coincides with the set of all space automorphisms that fix a finite subseries; this implies that the Hirsch–Plotkin radical is a Fitting group. Conversely, we prove that every countable Fitting group, which is either torsion-free or a p-group may be represented as a subgroup of the Hirsch–Plotkin radical of a series stabilizer.