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Relatively hyperbolic groups with strongly shortcut parabolics are strongly shortcut (2010.03421v3)
Published 7 Oct 2020 in math.GR
Abstract: We show that a group that is hyperbolic relative to strongly shortcut groups is itself strongly shortcut, thus obtaining new examples of strongly shortcut groups. The proof relies on a result of independent interest: we show that every relatively hyperbolic group acts properly and cocompactly on a graph in which the parabolic subgroups act properly and cocompactly on convex subgraphs.