Submission date: 9 September 2015.

Abstract:

We discuss the Bohr compactification of a pseudofinite group, motivated by a question of Boris Zilber. Basically referring to results in the literature we point out (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 a nonstandard model of set theory in which it is definable, is commutative-by-profinite.

Mathematics Subject Classification: 22C05, 20D05, 03C45, 03H05

Keywords and phrases:

Full text arXiv 1509.02895: pdf, ps