On the abelianization of a torsion free crystallographic group
A torsion free crystallographic group, which is also known as a Bieberbach group is a generalization of free abelian groups. It is an extension of a lattice group by a finite point group. The study of n-dimensional crystallographic group had been done by many researchers over a hundred years ago. A...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Penerbit UTM
2014
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/54313/1/NorHanizaSarmin2014_Ontheabelianizationofatorsion.pdf http://eprints.utm.my/id/eprint/54313/ http://dx.doi.org/10.11113/jt.v70.2424 |
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| Summary: | A torsion free crystallographic group, which is also known as a Bieberbach group is a generalization of free abelian groups. It is an extension of a lattice group by a finite point group. The study of n-dimensional crystallographic group had been done by many researchers over a hundred years ago. A Bieberbach group has been characterized as a fundamental group of compact, connected, flat Riemannian manifolds. In this paper, we characterize Bieberbach groups with trivial center as exactly those with finite abelianizations. The abelianization of a Bieberbach group is shown to be finite if the center of the group is trivial |
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