Work

Marton’s conjecture in abelian groups with bounded torsion

Year: 2026

Type: article

Abstract: We prove a Freiman–Ruzsa-type theorem with polynomial bounds in arbitrary abelian groups with bounded torsion, thereby proving (in full generality) a conjecture of Marton. Specifically, let G be an abelian group of torsion m (meaning m g = 0 for all g ∈ G ) and suppose that A is a non-empty subset of G with | A + A | ≤ K | A | . Then A can be covered by at most ( 2 K ) O ( m 3 ) translates of a subgroup H ≤ G of cardinality at most | A | . The argument is a variant of that used in the case G = F 2 n in a recent paper of the authors.

Source: Annales de la faculté des sciences de Toulouse Mathématiques

DOI: 10.5802/afst.1839

Authors: W. Timothy Gowers, Ben J. Green, Freddie Manners, Terence Tao

Institutions: Collège de France, University of Oxford, University of California San Diego, University of California, Los Angeles

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7123341060

FWCI: 36.25

Cites: 11

Cited by: 2

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