The Stabilized Automorphism Group of a Subshift

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.

Automated summary

In this study, we introduce the stabilization of the automorphism group for a mixing shift of finite type and investigate its algebraic properties. We are able to distinguish many of the stabilized automorphism groups using these properties. Additionally, for a full shift, we show that the subgroup generated by elements of finite order in the stabilized automorphism group is simple.