ON A CLASS OF AUTOMATA GROUPS GENERALIZING LAMPLIGHTER GROUPS
Pedro V. Silva, Benjamin Steinberg · International Journal of Algebra and Computation · 2005
We study automata groups generated by reset automata. Every lamplighter group ℤ/nℤ wr ℤ can be generated by such an automaton, and in general these automata groups are similar in nature to lamplighters: they are amenable locally-finite-by-cyclic groups; under mild decidable conditions, the semigroups generated by such automata are free. Parabolic subgroups and fractal properties are considered.