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Mappings of group shifts

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Abstract

A group shift is a proper closed shift-invariant subgroup ofG ℤ 2 whereG is a finite group. We consider a class of group shifts in whichG is a finite field and show that mixing is a necessary and sufficient condition on such a group shift for all codes from it into another group shift to be affine and all codes from another group shift into it to be affine. As a corollary, it will follow forG=ℤ p that two mixing group shifts are topologically conjugate if and only if they are equal.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, 38152-6429, Memphis, TN, USA

    Anthony N. Quas & Paul B. Trow

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  1. Anthony N. Quas
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  2. Paul B. Trow
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Correspondence to Anthony N. Quas.

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Quas, A.N., Trow, P.B. Mappings of group shifts. Isr. J. Math. 124, 333–365 (2001). https://doi.org/10.1007/BF02772629

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