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Pré-Publication, Document De Travail Année : 2023

SMALL DOUBLING IMPLIES SMALL TRIPLING AT LARGE SCALES

Résumé

We show that if K 1 is a parameter and S is a finite symmetric subset of a group containing the identity such |S 2n | K|S n | for some integer n 2K 2 , then |S 3n | exp(exp(O(K 2)))|S n |. Such a result was previously known only under the stronger assumption that |S 2n+1 | K|S n |. We prove similar results for locally compact groups and vertex-transitive graphs. We indicate some results in the structure theory of vertex-transitive graphs of polynomial growth whose hypotheses can be weakened as a result.
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Dates et versions

hal-04315602 , version 1 (30-11-2023)

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Romain Tessera, Matthew Tointon. SMALL DOUBLING IMPLIES SMALL TRIPLING AT LARGE SCALES. 2023. ⟨hal-04315602⟩
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