Wreath Product in Factorization of Holosymmetric Group |
| W. Florek and T. Lulek Institute of Physics, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland |
| Received: August 16, 1990 |
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| The holosymmetric group Q of an n-dimensional crystal lattice determined by a given lattice basis B is considered. This group is contained in the n-dimensional orthogonal group O(n) so its elements preserve the orthogonality of basis vectors and their lengths. These conditions yield the decomposition of lattice basis into orthogonal sublattices and next the factorization of the holosymmetric group, which can be written as a direct product of complete monomial groups of k-dimensional (k ≤ n) holosymmetric groups. Simple, decomposable and primitive holosymmetric groups are discussed. The results for n ≤ 4 are presented. |
| DOI: 10.12693/APhysPolA.79.843 PACS numbers: 61.50.Em, 02.20.+b |