格的相似与符合旋转
Similarity versus Coincidence Rotations of Lattices
摘要：
研究d维欧几里得空间中任意格L的相似旋转群和重合旋转群。证明了相似旋转群包含重合旋转作为一个正规子群。此外，相应的因素组的结构进行了检查。如果维数d是一个素数，这个因子群是一个初等阿贝尔d-群。此外，如果L是有理格，则因子群是平凡的（d奇数）或初等阿贝尔2-群（d偶数）。
英文摘要：
The groups of similarity and coincidence rotations of an arbitrary lattice L 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 L is a rational lattice, the factor group is trivial (d odd) or an elementary Abelian 2-group (d even).
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