In Chapters 2 and 3 of this thesis, we find the structure of all groups generated by an n-cycle and a 2-cycle or a 3-cycle. When these groups fail to be either Sn or An then we show that they form a certain wreath product or an extension of a wreath product. We also determine, in Chapters 4 and 5, the structure of all groups generated by an n-cycle and the product of two 2-cycles or a 4-cycle. The structure of these groups depends on the results obtained in the previous chapters. In Chapter 6 we give some general results of groups generated by an n-cycle and a k-cycle. In Chapter 7 we calculate the probability of generating a proper subgroup, other than the alternating group, by two elements one of which is an n-cyc1e and the other is chosen randomly. In Chapters 8 and 9 we give some of the programs written in GAP language, which used in the earlier work and which can be used by other workers in this area.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:636485 |
| Date | January 1993 |
| Creators | Al-Amri, Ibrahim Rasheed |
| Publisher | University of St Andrews |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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