  Let $H$ be a proper subgroup of a discrete group $G$. We introduce a notion
of relative inner amenability of $H$ in $G$, we prove some equivalent
conditions and provide examples as well as counter-examples. We also discuss
the corresponding relative property gamma for pairs of finite factors $N\subset
M$ and we deduce from this a characterization of discrete, icc groups which do
not have Kazhdan's property (T).
