发表机构
Università degli Studi di Milano-Bicocca; Université de Genève; Heinrich-Heine-Universität Düsseldorf; Université catholique de Louvain (IRMP); University of St Andrews; Western Sydney University; University of Lincoln; The University of Newcastle（米兰比可卡大学; 日内瓦大学; 杜塞尔多夫大学; 天主教鲁汶大学; 圣安德鲁斯大学; 西悉尼大学; 林肯大学; 纽卡斯尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文解决了局部紧群理论中的开放问题，证明非离散紧生成全不连通拓扑单群类中存在不可数多个（$2^{\aleph_0}$个）局部同构类，并概述了证明思路与来源。
AI 中文摘要
局部紧群理论中的一个主要开放问题如下。设$\mathscr{S}$为非离散紧生成全不连通局部紧且拓扑单的群类。$\mathscr{S}$中群的局部同构类的数量是否不可数？我们已回答了这个问题，证明了$\mathscr{S}$中存在$2^{\aleph_0}$个局部同构类。本预印本是即将发表的论文的概述。我们的结果未使用人工智能获得；它源于在马德里康普顿斯大学举办的“分支群：子群、刚性、拓扑”研讨会上的一个持续数天的问题讨论环节，该研讨会由Dominik Francoeur、Alejandra Garrido和Tatiana Nagnibeda组织。
英文摘要
A major open question in the theory of locally compact groups is the following. Let $\mathscr{S}$ be the class of non-discrete compactly generated totally disconnected locally compact groups that are topologically simple. Is the number of local isomorphism classes of groups in $\mathscr{S}$ uncountable? We have answered this question, showing that there are $2^{\aleph_0}$ local isomorphism classes in $\mathscr{S}$. Our result was obtained without the use of artificial intelligence; it arose from a problem session that ran over several days at the workshop "Branch groups: subgroups, rigidity, topologies" at the Universidad Complutense de Madrid, organised by Dominik Francoeur, Alejandra Garrido and Tatiana Nagnibeda.
CommentsDraft, includes full proof of the result (replacing the previous overview). No artificial intelligence was used to prove our result
