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Similarity and Coincidence Isometries for Modules

Published online by Cambridge University Press:  20 November 2018

Svenja Glied
Svenja Glied*
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, GermanyURL: http://www.math.uni-bielefeld.de/baake/ e-mail: sglied@math.uni-bielefeld.de
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Abstract

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The groups of (linear) similarity and coincidence isometries of certain modules $\Gamma $ in $d$-dimensional Euclidean space, which naturally occur in quasicrystallography, are considered. It is shown that the structure of the factor group of similarity modulo coincidence isometries is the direct sum of cyclic groups of prime power orders that divide $d$. In particular, if the dimension $d$ is a prime number $p$, the factor group is an elementary abelian $p$-group. This generalizes previous results obtained for lattices to situations relevant in quasicrystallography.

Keywords

20H1582D2552C23
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 1 , 01 March 2012 , pp. 98 - 107
Copyright
Copyright © Canadian Mathematical Society 2012

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