  In 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 $\Gamma$ for the group von Neumann
algebras involved. By a result of E.G.Effros, F(N) follows inner amenable.
