Amenable actions, free products and a fixed point property
نویسندگان
چکیده
منابع مشابه
Amenable Actions, Free Products and a Fixed Point Property
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 that kind. A complete characterization of such free products is given in terms of a fixed point property.
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We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such an action, which applies for example to surface groups and fundamental groups of surface bundles over S.
متن کامل2 00 9 Amenable actions of amalgamated free products
We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such an action, which applies for example to surface groups and fundamental groups of surface bundles over S.
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2006
ISSN: 0024-6093
DOI: 10.1112/blms/bdl011