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.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)