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A result of Gersten states that if is a hyperbolic group with integral cohomological dimension then every finitely presented subgroup is hyperbolic. We generalize this result for the rational case . In particular, the result applies to the class of torsion-free hyperbolic groups with and discovered by Bestvina and Mess.
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Shivam Arora, Eduardo Martínez-Pedroza, Subgroups of word hyperbolic groups in rational dimension 2. Groups Geom. Dyn. 15 (2021), no. 1, pp. 83–100DOI 10.4171/GGD/592