Familles de graphes expanseurs et paires de HeckeFamilies of expanding graphs and Hecke pairs |
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Authors: | MBachir Bekka Robyn Curtis Pierre de la Harpe |
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Institution: | 1. Département de mathématiques, Université de Metz, Ile du Saulcy, 57045 Metz, France;2. Section de mathématiques, Université de Genève, C.P. 240, CH-1211 Genève 24, Suisse |
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Abstract: | Let H be a subgroup of a group G. Suppose that (G,H) is a Hecke pair and that H is finitely generated by a finite symmetric set of size k. Then G/H can be seen as a graph (possibly with loops and multiple edges) whose connected components form a family (Xi)i∈I of finite k-regular graphs. In this Note, we analyse when the size of these graphs is bounded or tends to infinity and we present criteria for (Xi)i∈I to be a family of expanding graphs as well as some examples. To cite this article: M.B. Bekka et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 463–468. |
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