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Toeplitz subshift whose automorphism group is not finitely generated

Volume 146 / 2017

Ville Salo Colloquium Mathematicum 146 (2017), 53-76 MSC: Primary 37B10. DOI: 10.4064/cm6463-2-2016 Published online: 15 July 2016


We compute an explicit presentation of the (topological) automorphism group of a particular Toeplitz subshift with subquadratic complexity. The automorphism group is a non-finitely generated subgroup of rational numbers, or alternatively the $5$-adic integers, under addition, the shift map corresponding to the rational number 1. The group is $$ (\langle(5/2)^i \mid i \in \mathbb {N}\rangle , +) \leq (\mathbb {Q}, +). $$


  • Ville SaloCenter for Mathematical Modeling
    University of Chile
    Santiago, Chile

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