2024/12/25 by Alejandra Garrido, Garrido, Alejandra, Colin D. Reid +1 · 1 citation
Mathematics · #20E08 #20E32 #22D05 #22F50 #37B05 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2412.18891
openalex publication_date 2024/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we give sufficient conditions for a group to have simple derived subgroup; the argument is based on generalising properties observed for extremely proximal micro-supported actions on the Cantor space, and generalises previous results of Matui, Le Boudec and others in this direction. We give a sufficient condition for a non-trivial normal subgroup (not assumed closed) of a locally compact group G to be open, also based on the theory of micro-supported actions. This shows in particular that many of the class of robustly monolithic groups introduced by Caprace--Reid--Wesolek are simple-by-discrete.