2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71020In this paper we prove that the general version, F(N) of the Thompson group is inner amenable. As a consequence we generalize a result of P.Jolissaint. To do so, we prove first that F(N) together with a normal subgroup are i.c.c (infinite conjugacy classes) groups. Then, we investigate the relative McDuff property out of which we extract property $Γ$ for the group von Neumann algebras involved. By a result of E.G.Effros, F(N) follows inner amenable.A "Background" section has been added; to appear in Proceedings of the AMSOperator AlgebrasGroup Theory22D15text