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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-7,
author = {A. Ivanov},
title = {Strongly bounded automorphism groups},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {57-67},
zbl = {1098.20003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-7}
}
A. Ivanov. Strongly bounded automorphism groups. Colloquium Mathematicae, Tome 106 (2006) pp. 57-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-7/