Nous montrons qu'un graphe à croissance linéaire admet un nombre fini d'horofonctions. Cela donne une preuve courte et simple que chaque groupe infini de type fini à croissance linéaire est virtuellement cyclique.
We prove that a linear growth graph has finitely many horofunctions. This provides a short and simple proof that any finitely generated infinite group of linear growth is virtually cyclic.
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@article{CRMATH_2016__354_12_1151_0, author = {Tointon, Matthew C.H. and Yadin, Ariel}, title = {Horofunctions on graphs of linear growth}, journal = {Comptes Rendus. Math\'ematique}, pages = {1151--1154}, publisher = {Elsevier}, volume = {354}, number = {12}, year = {2016}, doi = {10.1016/j.crma.2016.10.015}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2016.10.015/} }
TY - JOUR AU - Tointon, Matthew C.H. AU - Yadin, Ariel TI - Horofunctions on graphs of linear growth JO - Comptes Rendus. Mathématique PY - 2016 SP - 1151 EP - 1154 VL - 354 IS - 12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2016.10.015/ DO - 10.1016/j.crma.2016.10.015 LA - en ID - CRMATH_2016__354_12_1151_0 ER -
%0 Journal Article %A Tointon, Matthew C.H. %A Yadin, Ariel %T Horofunctions on graphs of linear growth %J Comptes Rendus. Mathématique %D 2016 %P 1151-1154 %V 354 %N 12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2016.10.015/ %R 10.1016/j.crma.2016.10.015 %G en %F CRMATH_2016__354_12_1151_0
Tointon, Matthew C.H.; Yadin, Ariel. Horofunctions on graphs of linear growth. Comptes Rendus. Mathématique, Tome 354 (2016) no. 12, pp. 1151-1154. doi : 10.1016/j.crma.2016.10.015. http://archive.numdam.org/articles/10.1016/j.crma.2016.10.015/
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