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Search: MSC category 82D25 ( Crystals {For crystallographic group theory, see 20H15} )

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1. CMB 2011 (vol 55 pp. 98)

Glied, Svenja
Similarity and Coincidence Isometries for Modules
The groups of (linear) similarity and coincidence isometries of certain modules $\varGamma$ 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.

Categories:20H15, 82D25, 52C23

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