The automorphism group of a coded system

Fiebig, Doris; Fiebig, Ulf-Rainer

doi:10.1090/S0002-9947-96-01603-0

The automorphism group of a coded system
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by Doris Fiebig and Ulf-Rainer Fiebig

Trans. Amer. Math. Soc. 348 (1996), 3173-3191

DOI: https://doi.org/10.1090/S0002-9947-96-01603-0

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Abstract:

We give a general construction of coded systems with an automorphism group isomorphic to $\mathbf {Z}\oplus G$ where $G$ is any preassigned group which has a “continuous block presentation” (the isomorphism will map the shift to $(1,e_G))$. Several applications are given. In particular, we obtain automorphism groups of coded systems which are abelian, which are finitely generated and one which contains $\mathbf {Z}[1/2]$. We show that any group which occurs as a subgroup of the automorphism group of some subshift with periodic points dense already occurs for some synchronized system.

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