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arXiv · 1107.3955

Hirsch-Plotkin radical of stability groups

Carlo Casolo·Orazio Puglisi
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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.

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Carlo Casolo, Orazio Puglisi. 2011-07-20. Hirsch-Plotkin radical of stability groups. https://arxiv.org/abs/1107.3955

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