Abstract
We study finitely generated pairs of groups H ≤ G such that the Schreier graph of H has at least two ends and is narrow. Examples of narrow Schreier graphs include those that are quasi-isometric to finitely ended trees or have linear growth. Under this hypothesis, we show that H is a virtual fiber subgroup if and only if G contains infinitely many double cosets of H. Along the way, we prove that if a group acts essentially on a finite dimensional CAT(0) cube complex with no facing triples then it virtually surjects onto the integers with kernel commensurable to a hyperplane stabiliser.
Original language | English |
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Pages (from-to) | 3652--3668 |
Journal | Bulletin of the London Mathematical Society |
Volume | 56 |
Issue number | 12 |
Early online date | 4 Oct 2024 |
DOIs | |
Publication status | Published - 5 Dec 2024 |