Abstract
We prove Schlichting’s theorem for approximate subgroups: if \({\mathcal {X}}\) is a uniform family of commensurable approximate subgroups in some ambient group, then there exists an invariant approximate subgroup commensurable with \({\mathcal {X}}\).
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Notes
In this paper, we assume \(0\in {\mathbb {N}}\).
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Acknowledgements
The author wants to thank her supervisor Frank Wagner for suggesting this interesting topic and for his brilliant idea of going to the \(2^k\)-fold product of approximate subgroups to make the key lemma, Lemma 3.3, work. She also wants to thank the anonymous referee for lots of valuable advices and comments.
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This author is supported by the China Scholarship Council (Grant No. 201507720027) and partially supported by ValCoMo (ANR-13-BS01-0006).
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Zou, T. Schlichting’s theorem for approximate subgroups. Arch. Math. 114, 491–501 (2020). https://doi.org/10.1007/s00013-020-01435-6
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DOI: https://doi.org/10.1007/s00013-020-01435-6