Similarity and Coincidence Isometries for Modules

[摘要] The groups of (linear) similarity and coincidence isometries ofcertain modules $varGamma$ in $d$-dimensional Euclidean space, whichnaturally occur in quasicrystallography, are considered. It is shownthat the structure of the factor group of similarity modulocoincidence isometries is the direct sum of cyclic groups of primepower orders that divide $d$. In particular, if the dimension $d$ is aprime number $p$, the factor group is an elementary abelian$p$-group. This generalizes previous results obtained for lattices tosituations relevant in quasicrystallography.

[学科分类] 数学（综合）

[关键词] biharmonic operator;eigenvalue;eigenvector;inequality