Palindromic subshifts and simple periodic groups of intermediate growth

• 成果类型: Article
• 署名作者: Nekrashevych, Volodymyr
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2018.187.3.2
• 发表日期: 2018
• 页码: 667-719
• 关键词: topological full groups; schreier graphs; amenability; WORD; dimension; systems

摘要

We describe a new class of groups of Burnside type, by giving a procedure transforming an arbitrary non-free minimal action of the dihedral group on a Cantor set into an orbit-equivalent action of an infinite finitely generated periodic group. We show that if the associated Schreier graphs are linearly repetitive, then the group is of intermediate growth. In particular, this gives first examples of simple groups of intermediate growth.