Remarks on compactifications of pseudofinite groups
Volume 236 / 2017
Fundamenta Mathematicae 236 (2017), 193-200
MSC: Primary 03C20; Secondary 22C05.
DOI: 10.4064/fm275-7-2016
Published online: 26 August 2016
Abstract
We discuss the Bohr compactification of a pseudofinite group, motivated by a question of Boris Zilber. We point out that (i) the Bohr compactification of an ultraproduct of finite simple groups is trivial, and (ii) the “definable” Bohr compactification of any pseudofinite group $G$, relative to an ambient nonstandard model of set theory in which $G$ is definable, is commutative-by-profinite.
