The automorphism group of a coded system
Doris Fiebig, Ulf-Rainer Fiebig · Transactions of the American Mathematical Society · 1996
We give a general construction of coded systems with an automorphism group isomorphic to Z ⊕ G \mathbf {Z}\oplus G where G G is any preassigned group which has a “continuous block presentation” (the isomorphism will map the shift to ( 1 , e G ) ) (1,e_G)) . Several applications are given. In particular, we obtain automorphism groups of coded systems which are abelian, which are finitely generated and one which contains Z [ 1 / 2 ] \mathbf {Z}[1/2] . We show that any group which occurs as a subgroup of the automorphism group of some subshift with periodic points dense already occurs for some synchronized system.