The Lamplighter Group L2

Quadratic equations in the Grigorchuk group

“…History of the study of L 2 . The group L 2 was first studied under the name of the lamplighter group by Kaimanovich and Vershik [12], though it has been an object of study for much longer as a simple example of a wreath product (see [4] for a compact history). The standard lamplighter group L 2 has many different realizations, including as a dynamical system, an infinite direct sum, and notably as a self-similar group generated by a 2-state automaton (see Grigorchuk and Żuk [11]).…”