Growth of permutational extensions

• 成果类型: Article
• 署名作者: Bartholdi, Laurent; Erschler, Anna
• 署名单位: University of Gottingen; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0368-x
• 发表日期: 2012
• 页码: 431-455
• 关键词: intermediate; semigroups

摘要

We study the geometry of a class of group extensions, containing permutational wreath products, which we call permutational extensions. We construct for all k is an element of N a torsion group K-k with growth function upsilon K-k (n) similar to exp(n(1-(1-alpha)k)), 2(3-3/alpha) + 2(2-2/alpha) + 2(1-1/alpha) = 2, and a torsion-free group H-k with growth function upsilon H-k (n) similar to exp(log(n)n(1-(1-alpha)k)). These are the first examples of groups of intermediate growth for which the asymptotics of their growth function is known. We construct a group of intermediate growth that contains the group of finitely supported permutations of a countable set as a subgroup. This gives the first example of a group of intermediate growth containing an infinite simple group as a subgroup.