$C^{\ast }$-simplicity for groups with non-elementary convergence group actions

Abstract

We prove that a countable group with an effective minimal non-elementary convergence group action is a Powers group. More strongly we prove that it is a strongly Powers group and thus its non-trivial subnormal subgroups are $C^{\ast }$-simple.

7 pages

References in corpus (2)

• Relative hyperbolicity and relative quasiconvexity for countable groups
• C${}^{\ast }$-simple groups: amalgamated free products, HNN extensions, and fundamental groups of 3-manifolds