Zakaria, Mardhiah (2011) The commutativity degree of 3-engel groups up to order 40. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science.
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Abstract
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.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | Thesis (Sarjana Sains (Matematik)) - Universiti Teknologi Malaysia, 2011; Supervisor : Dr. Nor Muhainiah Mohd. Ali |
| Uncontrolled Keywords: | Engel’s theorem, Friedrich Engel, commutativity degree |
| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics > QA76 Computer software |
| Divisions: | Science |
| ID Code: | 47967 |
| Deposited By: | Narimah Nawil |
| Deposited On: | 08 Oct 2015 00:19 |
| Last Modified: | 30 May 2018 03:57 |
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