On the automorphism group of minimal S-adic subshifts of finite alphabet rank

It has been recently proved that the automorphism group of a minimal subshift with non-superlinear word complexity is virtually Z [Cyr and Kra. The automorphism group of a shift of linear growth: beyond transitivity. Forum Math. Sigma 3 (2015), e5; Donoso et al. On automorphism groups of low complexity subshifts. Ergod. Th. & Dynam. Sys. 36(1) (2016), 64-95]. In this article we extend this result to a broader class proving that the automorphism group of a minimal S-adic subshift of finite alphabet rank is virtually Z. The proof is based on a fine combinatorial analysis of the asymptotic classes in this type of subshifts, which we prove are a finite number.