We give a characterization for finite height subgroups in relatively hyperbolic groups by showing that a finitely generated, undistorted subgroup H of a relatively hyperbolic group (G, P) has finite height if and only H ∩ gPg^-1 has finite height in gPg^-1 for each conjugate of peripheral subgroup in P. Additionally, we prove that the concepts of finite height and strongly quasiconvexity are equivalent within the class of extended admissible groups. This class includes both the fundamental groups of non-geometric 3-mani-folds and Croke-Kleiner admissible groups.

We would like to thank Wenyuan Yang and Hung Cong Tran for their helpful conversations. The author was partially supported by the National Key Program for the development of Mathematics in the period from 2021 to 2030 under grant number B2024-CTT-04. We thank the referee for careful reading of the paper and for suggestions that improved the exposition.