Hirsch-Plotkin radical of stability groups

Details Hirsch-Plotkin radical of stability groups Hirsch-Plotkin radical of stability groups

2011-07-20

arxiv.org/abs/1107.3955v1

Mathematics

Group Theory

28 pages

Scientific paper

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 sub-series; this implies that the HP 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 HP radical of a series stabilizer.

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