发表机构
Institute for Advanced Study in Mathematics, Harbin Institute of Technology（哈尔滨工业大学高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了Caprace非内可均群的有限生成扩张，该扩张为GL_4(F_2(t))的ICC子群，无性质(T)，且非适当近端，从而解决了Boutonnet等人提出的问题。
AI 中文摘要
本文记录Caprace的非内可均群例子的一个有限生成扩张，该扩张也非适当近端，从而回答了Boutonnet、Ioana和Peterson的原始问题。该扩张是$\operatorname{GL}_4(\mathbb{F}_2(t))$的一个显式ICC子群，且无性质(T)。适当近端性的失效由Ishan-Peterson-Ruth的工作以及适当近端性对余可均子群的传递性得出。非内可均性由一个性质(T)子群和初等中心化子计算得出。
英文摘要
This note record a finitely generated extension of Caprace's example of a non-inner-amenable group is also not properly proximal, which answers the original question by Boutonnet, Ioana and Peterson. The extension is an explicit ICC subgroup of $\operatorname{GL}_4(\mathbb{F}_2(t))$, which has no property \textup{(T)}. Failure of proper proximality follows from the work of Ishan-Peterson-Ruth and the passage of proper proximality to co-amenable subgroups. Non-inner-amenability follows from a property-\textup{(T)} subgroup and an elementary centralizer computation.
