On the generalized membership problem in relatively hyperbolic groups

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Abstract

The aim of this note is to provide a proof of the decidability of the generalized membership problem for relatively quasi-convex subgroups of finitely presented relatively hyperbolic groups, under some reasonably mild conditions on the peripheral structure of these groups. These hypotheses are satisfied, in particular, by toral relatively hyperbolic groups.

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Kharlampovich, O., & Weil, P. (2020). On the generalized membership problem in relatively hyperbolic groups. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12180 LNCS, pp. 147–155). Springer. https://doi.org/10.1007/978-3-030-48006-6_11

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