Simple groups separated by finiteness properties

• 成果类型: Article
• 署名作者: Skipper, Rachel; Witzel, Stefan; Zaremsky, Matthew C. B.
• 署名单位: University of Gottingen; University of Bielefeld; State University of New York (SUNY) System; University at Albany, SUNY
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0835-8
• 发表日期: 2019
• 页码: 713-740
• 关键词: arithmetic groups; thompson groups; sigma-invariants

摘要

We show that for every positive integer n there exists a simple group that is of type Fn-1 but not of type Fn. For n3 these groups are the first known examples of this kind. They also provide infinitely many quasi-isometry classes of finitely presented simple groups. The only previously known infinite family of such classes, due to Caprace-Remy, consists of non-affine Kac-Moody groups over finite fields. Our examples arise from Rover-Nekrashevych groups, and contain free abelian groups of infinite rank.