Bernoulli disjointness and maximally almost periodic groups

TL;DR

This paper establishes conditions under which groups possess the Bernoulli Disjointness Property, linking group structure with dynamical properties like minimal free proximal flows.

Contribution

It introduces new criteria for groups to have the BDJ, connecting subgroup properties and dynamical flow characteristics.

Findings

Groups with infinite normal maximally almost periodic subgroups have BDJ.

Groups with sufficient infinite normal subgroups separating points have BDJ.

Groups with minimal free proximal flows have BDJ.

Abstract

We show that any discrete group containing an infinite, normal, maximally almost periodic subgroup has the Bernoulli Disjointness Property, or BDJ. Also, any group containing enough infinite normal subgroups to separate points has the BDJ. Lastly, any group admitting a minimal free proximal flow has the BDJ.