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Bulletin of the London Mathematical Society Advance Access originally published online on December 21, 2006
Bulletin of the London Mathematical Society 2007 39(1):138-150; doi:10.1112/blms/bdl011
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© 2006 London Mathematical Society

Amenable actions, free products and a fixed point property

Y. Glasner

University of Illinois at Chicago
Department of Mathematics
USA
yair{at}math.uic.edu

N. Monod

University of Chicago
Department of Mathematics
USA
monod{at}math.uchicago.edu

Received 10 May 2005. Revision received 17 January 2006.

We investigate the class of groups admitting an action on a set with an invariant mean. It turns out that many free products admit interesting actions of this kind. A complete characterization of such free products is given in terms of a fixed point property.

Current address: Department of Mathematics Ben Gurion University of the Neger Be’er Sheva 84105 Israel

Current address: Université de Genève Section de Mathématiques Switzerland nicolas.monod{at}unige.ch


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