Group theory analysis and formulation in rationalizing the crystallographic point groups
Group Theory is a powerful formal method for analyzing and rationalizing abstract and physical systems. In this research, group theory is used to rationalize the crystallographic point groups. This research focuses on Bieberbach group, that is a torsion free crystallographic group. Rationalizing...
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| Main Authors: | , , |
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| Format: | Monograph |
| Published: |
Universiti Pendidikan Sultan Idris
2009
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| Subjects: | |
| Online Access: | http://pustaka2.upsi.edu.my/eprints/430/ http://pustaka2.upsi.edu.my/eprints/430/1/GROUP%20THEORY%20ANALYSIS%20AND%20FORMULATION%20IN%20RATIONALIZING%20THE%20CRYSTALLOGRAPHIC%20POINT%20GROUPS.pdf |
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| Summary: | Group Theory is a powerful formal method for analyzing and rationalizing
abstract and physical systems. In this research, group theory is used to rationalize
the crystallographic point groups. This research focuses on Bieberbach group,
that is a torsion free crystallographic group. Rationalizing this Bieberbach
group means determining the group theory theories on constructing the group
for any point group P, determining the properties of the group and computing
the nonabelian tensor square of the group. In determining the theories on
constructing the Bieberbach group, n—dimension Bieberbach group with any
point group is considered. However, to determine the properties and to compute
the nonabelian tensor square of the group, only the centerless Bieberbach group
of dimension 4 with dihedral point group of order 8 is focused. Result shows that
there exists a Bieberbach group for any point group P if P is finite. Moreover, the
Bieberbach group of dimension 4 with dihedral point group of order 8 is proved
to be centerless torsion free group and is the extension of four copies of cyclic
group of infinite order by dihedral point group. It has a polycyclic presentation
and its' presentation is proved to be consistent polycyclic where with these facts
the nonabelian tensor square of this group is able to be computed by using the
method introduced by Blyth and Morse. |
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