Right amenable left group sets and the Tarski-Følner theorem

Document Type : Research Paper


Karlsruhe Institute of Technology


‎We introduce right amenability‎, ‎right FØlner nets‎, ‎and right paradoxical decompositions for left homogeneous spaces and prove the Tarski-FØlner theorem for left homogeneous spaces with finite stabilisers‎. ‎It states that right amenability‎, ‎the existence of right FØlner nets‎, ‎and the non-existence of right paradoxical decompositions are equivalent‎.


Main Subjects

[1] T. Ceccherini-Silberstein and M. Coornaert, Cellular Automata and Groups, 1-6, Computational complexity,
Springer, New York, 2010 336–349.
[2] E. Følner, On groups with full Banach mean value., Math. Scand., 3 (1955) 245–254.
[3] J. Neumann, Zur allgemeinen Theorie des Mas, Fund. Math., 13 (1929) 73–116.
[4] A. Tarski, Algebraische Fassung des Maßproblems, Fund. Math., 31 (1938) 207–223.
[5] S. Wacker, Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon Theorem, 1, Cellular Auto-mata and Discrete Complex Systems, (2016) 185–198.
[6] S. Wacker, The Garden of Eden Theorem for Cellular Automata on Group Sets, Cellular Automata, (2016) 66–78.