Groups isomorphic to all their non-trivial normal subgroups |
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| Authors: | Rüdiger Göbel Agnes T. Paras Saharon Shelah |
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| Affiliation: | (1) Department of Mathematics, Wesleyan University, 06459-0128 Middletown, CT, USA;(2) Department of Mathematics, Indiana University-Purdue University at Indianapolis, 46202-3216 Indianapolis, IN, USA;(3) Department of Mathematics, Hofstra University, 11549 Hempstead, NY, USA;(4) Department of Mathematics, University of California Davis, 95616 Davis, CA, USA |
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| Abstract: | A finite collectionP of finite sets tiles the integers iff the integers can be expressed as a disjoint union of translates of members ofP. We associate with such a tiling a doubly infinite sequence with entries fromP. The set of all such sequences is a sofic system, called a tiling system. We show that, up to powers of the shift, every shift of finite type can be realized as a tiling system. Some of this work was done at the Mathematical Sciences Research Institute (MSRI), where research is supported in part by NSF grant DMS-9701755. The first two authors thank K. Schmidt for useful conversations and ideas. |
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