We show that there exists a finitely generated group of growth for all functions satisfying for all large enough and the positive root of . Set ; then all functions that grow uniformly faster than are realizable as the growth of a group.
We also give a family of sum-contracting branched groups of growth for a dense set of .
Nous montrons qu’il existe un groupe de type fini de croissance pour n’importe quelle fonction satisfaisant lorsque est suffisamment grand, avec la racine positive de . Soit ; alors toutes les fonctions qui croissent uniformément plus vite que sont réalisables comme fonction de croissance d’un groupe.
Nous exhibons aussi une famille de groupes branchés contractants-pour-la-somme et de croissance , pour un sous-ensemble dense d’.
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
@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}, pages = {2003--2036}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {5}, year = {2014}, doi = {10.5802/aif.2902}, mrnumber = {3330929}, zbl = {06387329}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2902/} }
TY - JOUR AU - Bartholdi, Laurent AU - Erschler, Anna TI - Groups of given intermediate word growth JO - Annales de l'Institut Fourier PY - 2014 SP - 2003 EP - 2036 VL - 64 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2902/ DO - 10.5802/aif.2902 LA - en ID - AIF_2014__64_5_2003_0 ER -
%0 Journal Article %A Bartholdi, Laurent %A Erschler, Anna %T Groups of given intermediate word growth %J Annales de l'Institut Fourier %D 2014 %P 2003-2036 %V 64 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2902/ %R 10.5802/aif.2902 %G en %F AIF_2014__64_5_2003_0
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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