Similarity versus coincidence rotations of lattices

Glied, Svenja and Baake, Michael (2008). Similarity versus coincidence rotations of lattices. Zeitschrift für Kristallographie, 223(11-12) pp. 770–772.

DOI: https://doi.org/10.1524/zkri.2008.1054

Abstract

The groups of similarity and coincidence rotations of an arbitrary lattice Γ in d-dimensional Euclidean space are considered. It is shown that the group of similarity rotations contains the coincidence rotations as a normal subgroup. Furthermore, the structure of the corresponding factor group is examined. If the dimension d is a prime number, this factor group is an elementary Abelian d-group. Moreover, if Γ is a rational lattice, the factor group is trivial (d odd) or an elementary Abelian 2-group (d even).

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