Strongly bounded automorphism groups
Volume 105 / 2006
Colloquium Mathematicum 105 (2006), 57-67
MSC: 20F50, 03C60, 20E08.
DOI: 10.4064/cm105-1-7
Abstract
A group $G$ is strongly bounded if every isometric action of $G$ on a metric space has bounded orbits. We show that the automorphism groups of typical countable structures with the small index property are strongly bounded. In particular we show that this is the case when $G$ is the automorphism group of the countable universal locally finite extension of a periodic abelian group.
