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arXiv · 2412.18891

Compressible subgroups and simplicity

Alejandra Garrido·Colin D. Reid
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Abstract

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.

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Alejandra Garrido, Colin D. Reid. 2024-12-25. Compressible subgroups and simplicity. https://arxiv.org/abs/2412.18891

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