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Document Type |
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Thesis |
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Document Title |
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Regular Near Hexagons and Related Groups or Designs المنظم بقرب السداسي أو التصاميم المتعلقة |
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Subject |
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Mathematics |
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Document Language |
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Arabic |
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Abstract |
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The concept of a near 2n-gon is due to Shult and Yanushka [20]. Near 2n-gons are essentially a linear incidence system of points and lines. A near 2n-gon ( , L) has order (s, t) if each point lies on 1 + t lines and each line contains 1 + s points. A near 2n-gon of order (s, t) is called regular with parameters (s, t2, t3, … tn = t) if, whenever two points p and q are at distance d (1 ? d ? n), then exactly 1 + td lines through q carry points at distance d – 1 from p. The thesis comprises into four chapters. The first chapter is introductory and gives some basic definitions, terminology and preliminary concepts. In the second chapter we list some known results about regular 2n-gons with n = 2, 3, 4. In the third chapter we find eleven necessary conditions for the existence of a regular near hexagon and classify the following: (a) Thin near hexagons and related designs. (b) Near hexagons of Hamming type and their existence. (c) Classical near hexagons and the related classical simple groups. In the fourth chapter we discuss sporadic near hexagons. We obtain twelve feasible parameter sets for s = kt2, 1 ? k ? 5. Out of these twelve cases, we find some realizable regular near hexagons. In some cases, near hexagons do not exists and the remaining cases are still undecided |
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Supervisor |
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Dr. Saeed Ahmad Shad |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1426 AH
2005 AD |
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Added Date |
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Wednesday, June 11, 2008 |
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Researchers
| عبير سعد الغامدي | Al-Ghamdi, Abeer Saad | Researcher | Master | |
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Files
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23690.pdf
| pdf | المستخلص |
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23691.pdf
| pdf | Abstract |
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