We introduce a relative fixed point property for subgroups of a locally compact group, which we call relative amenability. It is a priori weaker than amenability. We establish equivalent conditions, related among others to a problem studied by Reiter in 1968. We record a solution to Reiter's problem.
We study the class of groups in which relative amenability is equivalent to amenability for all closed subgroups; we prove that contains all familiar groups. Actually, no group is known to lie outside .
Since relative amenability is closed under Chabauty limits, it follows that any Chabauty limit of amenable subgroups remains amenable if the ambient group belongs to the vast class .
Cite this article
Pierre-Emmanuel Caprace, Nicolas Monod, Relative amenability. Groups Geom. Dyn. 8 (2014), no. 3, pp. 747–774DOI 10.4171/GGD/246