Hirsch-Plotkin radical of stability groups
Group Theory
2011-07-21 v1
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 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.
Keywords
Cite
@article{arxiv.1107.3955,
title = {Hirsch-Plotkin radical of stability groups},
author = {Carlo Casolo and Orazio Puglisi},
journal= {arXiv preprint arXiv:1107.3955},
year = {2011}
}
Comments
28 pages