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| Pakistan Research Repository | Home |
Title of Thesis |
| Author(s) Muhammad Aslam |
| Institute/University/Department Details Department of Mathematics/ Quaid-i-Azam University, Islamabad |
| Session 2004 |
| Subject Mathematics |
| Number of Pages 98 |
| Keywords (Extracted from title, table of contents and abstract of thesis) linear groups, quadratic fields, finite fields, group g6,6(2,z),coset diagrams, homomorphisms |
Abstract |
| Download Full Thesis |  1267.87 KB |
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| S. No. | Chapter | Title of the Chapters | Page | Size (KB) |
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| 1 | 0 | Contents | 01 | 185.54 KB |
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| 2 | 1 | Preliminaries | 05 | 194.63 KB |
| 1.1 | Group Actions | 05 | ||
| 1.2 | Quadratic Fields | 06 | ||
| 1.3 | Finite Fields | 07 | ||
| 1.4 | A Projective Line Over the Finite Field | 09 | ||
| 1.5 | Linear Groups | 10 | ||
| 1.6 | The Group G6 ,6 (2,Z) | 13 | ||
| 1.7 | Coset Diagrams | 14 | ||
| 1.8 | Coset Diagrams for the Group G6 ,6 (2, Z) | 19 | ||
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| 3 | 2 | Action Of G6 ,6 (2,Z) On Real Quadratic Fields | 21 | 408.69 KB |
| 2.1 | Introduction | 21 | ||
| 2.2 | Existence of Ambiguous Numbers | 24 | ||
| 2.3 | Existence of Closed Paths | 38 | ||
| 2.4 | Intransitive Action of G6 ,6 (2,Z) | 43 | ||
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| 4 | 3 | Action Of G6 ,6 (2,Z) On Imaginary Quadratic Fields | 47 | 343.28 KB |
| 3.1 | Introduction | 47 | ||
| 3.2 | Existence of Fixed Points in Q .( j=n) | 49 | ||
| 3.3 | Orbits of Q. ( F3 ) | 50 | ||
| 3.4 | Orbits of Q. (j=n) | 57 | ||
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| 5 | 4 | ∆( 6,6,K) & Parametrization Of Actions Of G6,6(2,Z) | 66 | 245.92 KB |
| 4.1 | Introduction | 66 | ||
| 4.2 | Parameters for the Conjugacy Classes of G6 ,6 (2, Z) | 68 | ||
| 4.3 | Parametrization of the Actions of ∆ (6 ,6,k ) | 72 | ||
| 4.4 | Parametrization of the Actions of ∆ (6 ,6,k ;n) | 75 | ||
| 4.5 | Conjugacy Classes of the Non-degenerate Homomorphisms | 79 | ||
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