- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:00
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
8
2014
3
Relative amenability
Pierre-Emmanuel
Caprace
Université Catholique de Louvain, LOUVAIN-LA-NEUVE, BELGIUM
Nicolas
Monod
Ecole Polytechnique Fédérale de Lausanne, LAUSANNE, SWITZERLAND
Amenability, subgroups, Chabauty topology, approximate identity
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 $\mathscr{X}$ of groups in which relative amenability is equivalent to amenability for all closed subgroups; we prove that $\mathscr{X}$ contains all familiar groups. Actually, no group is known to lie outside $\mathscr{X}$. 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 $\mathscr{X}$.
General
747
774
10.4171/GGD/246
http://www.ems-ph.org/doi/10.4171/GGD/246