2024/02/29 by Azuelos, Pénélope
#20F65 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2402.19000
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.