Groups of given intermediate word growth
Annales de l'Institut Fourier, Volume 64 (2014) no. 5, pp. 2003-2036.

We show that there exists a finitely generated group of growth f for all functions f: + + satisfying f(2R)f(R) 2 f(η + R) for all R large enough and η + 2.4675 the positive root of X 3 -X 2 -2X-4. Set α - =log2/logη + 0.7674; then all functions that grow uniformly faster than exp(R α - ) are realizable as the growth of a group.

We also give a family of sum-contracting branched groups of growth exp(R α ) for a dense set of α[α - ,1].

Nous montrons qu’il existe un groupe de type fini de croissance f pour n’importe quelle fonction f: + + satisfaisant f(2R)f(R) 2 f(η + R) lorsque R est suffisamment grand, avec η + 2.4675 la racine positive de X 3 -X 2 -2X-4. Soit α - =log2/logη + 0.7674  ; alors toutes les fonctions qui croissent uniformément plus vite que exp(R α - ) sont réalisables comme fonction de croissance d’un groupe.

Nous exhibons aussi une famille de groupes branchés contractants-pour-la-somme et de croissance exp(R α ), pour un sous-ensemble dense d’α[α - ,1].

DOI: 10.5802/aif.2902
Classification: 20E08, 20F65
Keywords: Growth of groups, self-similar groups, groups acting on trees, wreath products
Mot clés : Croissance des groupes, groupes auto-similaires, groupes agissant sur des arbres, produits en couronne
Bartholdi, Laurent 1; Erschler, Anna 2

1 Georg-August Universität L.B.: Mathematisches Institut Bunsenstraße 3–5 D-37073 Göttingen (Germany)
2 A.E.: C.N.R.S. Université Paris Sud Département de Mathématiques Bâtiment 425 91405 Orsay (France)
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Bartholdi, Laurent; Erschler, Anna. Groups of given intermediate word growth. Annales de l'Institut Fourier, Volume 64 (2014) no. 5, pp. 2003-2036. doi : 10.5802/aif.2902. https://aif.centre-mersenne.org/articles/10.5802/aif.2902/

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