The commutativity degree of 3-engel groups up to order 40
Friedrich Engel has discovered Engel groups in the 50s in Germany. The origin of this group lies in the theory of Lie algebras. As an example, one of the basic classical results for Engel Lie algebras is Engel’s theorem. In this research, the 3- Engel groups of order up to 40 will be the main focus....
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| Format: | Thesis |
| Language: | English |
| Published: |
2011
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/47967/25/MardhiahZakariaMFS2011.pdf |
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| Summary: | Friedrich Engel has discovered Engel groups in the 50s in Germany. The origin of this group lies in the theory of Lie algebras. As an example, one of the basic classical results for Engel Lie algebras is Engel’s theorem. In this research, the 3- Engel groups of order up to 40 will be the main focus. An application of 3-Engel groups on probability theory will be presented too. The commutativity degree can also be viewed as the probability that two elements in the group commute denoted by . This probability applied to the eighteen 3-Engel groups with order at most 40 is proven to be at most 5/8. A software named Groups, Algorithms and Programming (GAP) software is used to facilitate most of the calculations in this research. |
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