Abstract
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.
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