The automorphism group of a shift of subquadratic growth

Van Cyr, Bryna Kra

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length n. When this complexity grows exponentially, the automorphism group has been shown to be large for various classes of subshifts. In contrast, we show that subquadratic growth of the complexity implies that for a topologically transitive shift X, the automorphism group Aut(X) is small: if H is the subgroup of Aut(X) generated by the shift, then Aut(X)/H is periodic. For linear growth, we show the stronger result that Aut(X)/H is a group of finite exponent.

Original languageEnglish (US)
Pages (from-to)613-621
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - Feb 2016


  • Automorphism
  • Block complexity
  • Subshift

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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