The Lamplighter Group L2
- 5k Downloads
The Lamplighter group L2 can be realized in different ways. We construct several groups whose elements are very different, yet which can be considered the same group, L2, because they are isomorphic and they can all be presented in the same way. We give a description of L2 as a dynamical system, as a group using an infinite direct sum in its definition and as a self-similar group generated by a 2-state automaton, as shown by R. Grigorchuk and A. Żuk.
- 4.Atiyah, M.F.: Elliptic operators, discrete groups and von Neumann algebras, Colloque Analyse et Topologie en l’Honneur de Henri Cartan (Orsay, 1974), Paris, Soc. Math. France. pp. 43–72. Astérisque, No., (1976), 32–33Google Scholar
- 26.Cleary, S., Taback, J.: Metric properties of the lamplighter group as an automata group. In: Geometric Methods in Group Theory, V. Contemporary Mathematics, vol. 372, pp. 207–218. American Mathematical Society, Providence (2005)Google Scholar
- 66.Nekrashevych, V.: Self-Similar Groups, pp. 9–23. American Mathematical Society, Providence (2005)Google Scholar
- 82.Warshall, A.: Strongly t-logarithmic t-generating sets: geometric properties of some soluble groups. arXiv:0808.2789 (2008)Google Scholar