The generalized dihedral groups Dih(Zn) as groups generated by time-varying automata

Abstract

Let Zn be a cubical lattice in the Euclidean space Rn. The generalized dihedral group Dih(Zn) is a topologically discrete group of isometries of Zn generated by translations and reflections in all points from Zn. We study this group as a group generated by a (2n+2)-state time-varying automaton over the changing alphabet. The corresponding action on the set of words is described.