Strongly bounded groups and infinite powers of finite groups
Group Theory
2010-08-04 v6 Logic
Abstract
We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently introduced by G. Bergman. Our main result is that G^I is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that omega_1-existentially closed groups are strongly bounded.
Cite
@article{arxiv.math/0411466,
title = {Strongly bounded groups and infinite powers of finite groups},
author = {Yves de Cornulier},
journal= {arXiv preprint arXiv:math/0411466},
year = {2010}
}
Comments
10 pages, no figure. Versions 1-3 were entitled "Uncountable groups with Property (FH)". To appear in Comm. Algebra