2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94753We present sufficient conditions for HNN extensions to be inner amenable, respectively ICC, which give necessary and sufficient criteria among Baumslag-Solitar groups. We deduce that such a group, viewed as acting on its Bass-Serre tree, contains non trivial elements which fix unbounded subtrees.16 pages, in french. Slightly stronger results and typographic corrections. To appear in Ann. Inst. Fourier (Grenoble)Group Theory20E06; 20E08; 20E45text