TY - JOUR AU - Jolissaint, Paul PY - 2016/11/01 Y2 - 2024/03/28 TI - Relative Inner Amenability and Relative Property Gamma JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 119 IS - 2 SE - Articles DO - 10.7146/math.scand.a-24748 UR - https://www.mscand.dk/article/view/24748 SP - 293-319 AB - 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 coming mainly from semidirect products, as well as counter-examples. We also discuss the corresponding relative property gamma for pairs of type II$_1$ factors $N\subset M$ and we deduce from this a characterization of discrete, icc groups which do not have property (T). ER -