Determination of symmetry groups of 2-generator 2- groups of class two and their rationalization in molecular vibration
Symmetry groups are powerful tools for describing the structure in physical system. The symmetry group which is composed of reflections and rotations is known as a point group. The space group of a crystal or crystallographic group is a mathematical description of the symmetry inherent in the struct...
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my.utm.91292017-08-14T08:00:22Z http://eprints.utm.my/id/eprint/9129/ Determination of symmetry groups of 2-generator 2- groups of class two and their rationalization in molecular vibration Aris, Nor'aini Sarmin, Nor Haniza Ahmad, Satapah Masri, Rohaidah Symmetry groups are powerful tools for describing the structure in physical system. The symmetry group which is composed of reflections and rotations is known as a point group. The space group of a crystal or crystallographic group is a mathematical description of the symmetry inherent in the structure. A crystallographic group G is a group extension of a group P by a free abelian group V of finite rank d. Hence there is a short exact sequence of the form 0 → V → G → P → 1. The group V is called the lattice subgroup and P is called the point group of G. The rank d of V is called the dimension the G. The Bieberbach groups are torsion free crystallographic groups. In this research, the Bieberbach groups with cyclic point group C2 up to six dimensions are considered. These groups are metabelian polycyclic groups. From the computation, there are exactly 11 non-isomorphic families Bieberbach groups when P is cyclic group of order 2 (up to dimension 6) and their group representations, which are consistent to the polycyclic representations, are obtained. Using GAP software, the matrix groups of these families are converted into finitely presented groups and polycyclic groups. These groups are investigated based on their nonabelian tensor square. By using a theory for computing the nonabelian tensor squares of polycyclic groups developed by Blyth and Morse (2008), some of properties of nonabelian tensor squares of these groups have been obtained and successfully and generalized to n dimension. Faculty of Science 2008-12-31 Monograph NonPeerReviewed Aris, Nor'aini and Sarmin, Nor Haniza and Ahmad, Satapah and Masri, Rohaidah (2008) Determination of symmetry groups of 2-generator 2- groups of class two and their rationalization in molecular vibration. Project Report. Faculty of Science, Skudai, Johor. (Unpublished) |
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Symmetry groups are powerful tools for describing the structure in physical system. The symmetry group which is composed of reflections and rotations is known as a point group. The space group of a crystal or crystallographic group is a mathematical description of the symmetry inherent in the structure. A crystallographic group G is a group extension of a group P by a free abelian group V of finite rank d. Hence there is a short exact sequence of the form 0 → V → G → P → 1. The group V is called the lattice subgroup and P is called the point group of G. The rank d of V is called the dimension the G. The Bieberbach groups are torsion free crystallographic groups. In this research, the Bieberbach groups with cyclic point group C2 up to six dimensions are considered. These groups are metabelian polycyclic groups. From the computation, there are exactly 11 non-isomorphic families Bieberbach groups when P is cyclic group of order 2 (up to dimension 6) and their group representations, which are consistent to the polycyclic representations, are obtained. Using GAP software, the matrix groups of these families are converted into finitely presented groups and polycyclic groups. These groups are investigated based on their nonabelian tensor square. By using a theory for computing the nonabelian tensor squares of polycyclic groups developed by Blyth and Morse (2008), some of properties of nonabelian tensor squares of these groups have been obtained and successfully and generalized to n dimension. |
| format |
Monograph |
| author |
Aris, Nor'aini Sarmin, Nor Haniza Ahmad, Satapah Masri, Rohaidah |
| spellingShingle |
Aris, Nor'aini Sarmin, Nor Haniza Ahmad, Satapah Masri, Rohaidah Determination of symmetry groups of 2-generator 2- groups of class two and their rationalization in molecular vibration |
| author_facet |
Aris, Nor'aini Sarmin, Nor Haniza Ahmad, Satapah Masri, Rohaidah |
| author_sort |
Aris, Nor'aini |
| title |
Determination of symmetry groups of 2-generator 2- groups of class two and their rationalization in molecular vibration |
| title_short |
Determination of symmetry groups of 2-generator 2- groups of class two and their rationalization in molecular vibration |
| title_full |
Determination of symmetry groups of 2-generator 2- groups of class two and their rationalization in molecular vibration |
| title_fullStr |
Determination of symmetry groups of 2-generator 2- groups of class two and their rationalization in molecular vibration |
| title_full_unstemmed |
Determination of symmetry groups of 2-generator 2- groups of class two and their rationalization in molecular vibration |
| title_sort |
determination of symmetry groups of 2-generator 2- groups of class two and their rationalization in molecular vibration |
| publisher |
Faculty of Science |
| publishDate |
2008 |
| url |
http://eprints.utm.my/id/eprint/9129/ |
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1643645124231561216 |
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13.211869 |