| Résume | The Haagerup property (a.k.a. a-(T)-menability) is a weak form of amenability. In a countable group, every Haagerup subgroup is contained in a maximal Haagerup subgroup, by Zorn's lemma. The study of maximal Haagerup subgroups of a given group was initiated in 2021 by Y. Jiang and A. Skalski, who classified maximal Haagerup subgroups in $\Z^2\rtimes GL_2(\Z)$. By simplifying the original proof we are able to extend it to more general semi-direct products. |
