2020/12/18 by Salo, Ville
#Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2012.10186
We prove that the set of subgroups of the automorphism group of a two-sided full shift is closed under countable graph products. We introduce the notion of a group action without A-cancellation (for an abelian group A), and show that when A is a finite abelian group and G is a group of cellular automata whose action does not have A-cancellation, the wreath product A \wr G embeds in the automorphism group of a full shift. We show that all free abelian groups and free groups admit such cellular automata actions. In the one-sided case, we prove variants of these results with reasonable alphabet blow-ups.