Groups of given intermediate word growth  [ Groupes de croissance intermédiaire donnée ]
Annales de l'Institut Fourier, Tome 64 (2014) no. 5, p. 2003-2036
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].
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].
DOI : https://doi.org/10.5802/aif.2902
Classification:  20E08,  20F65
Mots clés: Croissance des groupes, groupes auto-similaires, groupes agissant sur des arbres, produits en couronne
@article{AIF_2014__64_5_2003_0,
     author = {Bartholdi, Laurent and Erschler, Anna},
     title = {Groups of given intermediate word growth},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {5},
     year = {2014},
     pages = {2003-2036},
     doi = {10.5802/aif.2902},
     mrnumber = {3330929},
     zbl = {06387329},
     language = {en},
     url = {http://http://www.numdam.org/item/AIF_2014__64_5_2003_0}
}
Bartholdi, Laurent; Erschler, Anna. Groups of given intermediate word growth. Annales de l'Institut Fourier, Tome 64 (2014) no. 5, pp. 2003-2036. doi : 10.5802/aif.2902. http://www.numdam.org/item/AIF_2014__64_5_2003_0/

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