A note on nonabelian Freiman-Ruzsa
Sean Eberhard
TL;DR
This paper refines and simplifies the construction demonstrating that a certain formulation of the polynomial Freiman-Ruzsa conjecture does not hold in nonabelian groups.
Contribution
It improves and simplifies Breuillard and Tointon's recent construction showing the failure of the conjecture in nonabelian groups.
Findings
The polynomial Freiman-Ruzsa conjecture formulation fails in nonabelian groups.
Simplified construction makes the failure more accessible.
Strengthens understanding of additive combinatorics in nonabelian settings.
Abstract
Recently Breuillard and Tointon showed that one reasonable formulation of the polynomial Freiman-Ruzsa conjecture fails for nonabelian groups. We improve and simplify their construction.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces