The Stabilized Automorphism Group of a Subshift

Yair Israel Hartman, Bryna Kra*, Scott Edward Schmieding

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group, study its algebraic properties, and use them to distinguish many of the stabilized automorphism groups. We also show that for a full shift, the subgroup of the stabilized automorphism group generated by elements of finite order is simple and that the stabilized automorphism group is an extension of a free abelian group of finite rank by this simple group.

Original languageEnglish (US)
Pages (from-to)17112-17186
Number of pages75
JournalInternational Mathematics Research Notices
Issue number21
StatePublished - Nov 1 2022

ASJC Scopus subject areas

  • Mathematics(all)


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