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Abstracts
We consider connections between similar sublattices and coincidence site lattices and, more generally, between similar submodules and coincidence site modules of general (free) ℤ-modules in ℝ^d. In particular, we generalise results obtained by S. Glied and M. Baake on similarity and coincidence isometries of lattices and certain lattice-like modules called S-modules. An important result is that the factor group OS(M)/OC(M) is Abelian for arbitrary ℤ-modules M, where OS(M) and OC(M) are the groups of similar and coincidence isometries, respectively. In addition, we derive various relations between the indices of coincidence site lattices and their corresponding similar sublattices.
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Journal
Year
Volume
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Pages
641-644
Physical description
Dates
published
2014-08
Contributors
author
- Fakultät für Mathematik, Universität Bielefeld, 33615 Bielefeld, Germany
References
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Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv126n254kz