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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The automorphism group of a coded system


Authors: Doris Fiebig and Ulf-Rainer Fiebig
Journal: Trans. Amer. Math. Soc. 348 (1996), 3173-3191
MSC (1991): Primary 58F03, 20B27; Secondary 20E26
MathSciNet review: 1348860
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Abstract: We give a general construction of coded systems with an automorphism group isomorphic to $\mathbf Z\oplus G$ where $G$ is any preassigned group which has a ``continuous block presentation'' (the isomorphism will map the shift to $(1,e_G))$. Several applications are given. In particular, we obtain automorphism groups of coded systems which are abelian, which are finitely generated and one which contains $\mathbf Z[1/2]$. 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.


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Additional Information

Doris Fiebig
Affiliation: Institut für Angewandte Mathematik, Universität Heidelberg, im Neuenheimer Feld 294, 69120 Heidelberg, Germany
Email: Fiebig@math.uni-heidelberg.de

Ulf-Rainer Fiebig
Affiliation: Institut für Angewandte Mathematik, Universität Heidelberg, im Neuenheimer Feld 294, 69120 Heidelberg, Germany
Email: Fiebig@math.uni-heidelberg.de

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01603-0
PII: S 0002-9947(96)01603-0
Received by editor(s): December 13, 1994
Received by editor(s) in revised form: July 17, 1995
Article copyright: © Copyright 1996 American Mathematical Society