English

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

R2 v1 2026-06-21T18:39:21.809Z