Groups, Geometry, and Dynamics


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Volume 11, Issue 1, 2017, pp. 95–104
DOI: 10.4171/GGD/389

Published online: 2017-04-20

A note on relative amenability

Phillip Wesolek[1]

(1) University of Illinois-Chicago, USA

P.-E. Caprace and N. Monod isolate the class $\mathscr{X}$ of locally compact groups for which relatively amenable closed subgroups are amenable. It is unknown if $\mathscr X$ is closed under group extension. In this note, we exhibit a large, group extension stable subclass of $\mathscr X$, which suggests $\mathscr X$ is indeed closed under group extension. Along the way, we produce generalizations of the class of elementary groups and obtain information on groups outside $\mathscr X$.

Keywords: Amenability, relative amenability, elementary groups.

Wesolek Phillip: A note on relative amenability. Groups Geom. Dyn. 11 (2017), 95-104. doi: 10.4171/GGD/389