This article is cited in 4 papers

RESEARCH ARTICLE

The generalized dihedral groups $Dih(\mathbb{Z}^n)$ as groups generated by time-varying automata

Adam Woryna

Institute of Mathematics, Silesian University of Technology, 44–100 Gliwice

Abstract: Let $\mathbb{Z}^n$ be a cubical lattice in the Euclidean space $\mathbb{R}^n$. The generalized dihedral group $Dih(\mathbb{Z}^n)$ is a topologically discrete group of isometries of $\mathbb{Z}^n$ generated by translations and reflections in all points from $\mathbb{Z}^n$. 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.

Keywords: generalized dihedral groups, time-varying automaton, group generated by time-varying automaton.

MSC: 20E22, 20E08, 20F65

Received: 23.09.2006
Revised: 14.10.2008

Language: English

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