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Remarks on compactifications of pseudofinite groups

Volume 236 / 2017

Anand Pillay Fundamenta Mathematicae 236 (2017), 193-200 MSC: Primary 03C20; Secondary 22C05. DOI: 10.4064/fm275-7-2016 Published online: 26 August 2016


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.


  • Anand PillayDepartment of Mathematics
    University of Notre Dame
    Notre Dame, IN 46556, U.S.A.

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