Geodesic
The generalized dihedral groups $Dih(\mathbb{Z}^n)$ as groups generated by time-varying automata
Algebra and discrete mathematics, no. 3 (2008), pp. 98-111

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ADM_2008_3_a7,
     author = {Adam Woryna},
     title = {The generalized dihedral groups $Dih(\mathbb{Z}^n)$ as groups generated by time-varying automata},
     journal = {Algebra and discrete mathematics},
     pages = {98--111},
     publisher = {mathdoc},
     number = {3},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2008_3_a7/}
}
TY  - JOUR
AU  - Adam Woryna
TI  - The generalized dihedral groups $Dih(\mathbb{Z}^n)$ as groups generated by time-varying automata
JO  - Algebra and discrete mathematics
PY  - 2008
SP  - 98
EP  - 111
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2008_3_a7/
LA  - en
ID  - ADM_2008_3_a7
ER  - 
%0 Journal Article
%A Adam Woryna
%T The generalized dihedral groups $Dih(\mathbb{Z}^n)$ as groups generated by time-varying automata
%J Algebra and discrete mathematics
%D 2008
%P 98-111
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2008_3_a7/
%G en
%F ADM_2008_3_a7
Adam Woryna. The generalized dihedral groups $Dih(\mathbb{Z}^n)$ as groups generated by time-varying automata. Algebra and discrete mathematics, no. 3 (2008), pp. 98-111. http://geodesic.mathdoc.fr/item/ADM_2008_3_a7/