Mathematics – Group Theory
Scientific paper
2008-10-14
Mathematics
Group Theory
Minor corrections. To appear in Groups, Geometry and Dynamics.
Scientific paper
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 $\mathbb{S}^1$.
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