I= LINEAR GROUPS AND THEIR ACTIONS ON CERTAIN FIELDS
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Title of Thesis
LINEAR GROUPS AND THEIR ACTIONS ON CERTAIN FIELDS

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
No Abstract

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1267.87 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents 01
185.54 KB
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
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
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
5 4 ˆ†( 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 ˆ† (6 ,6,k ) 72
  4.4 Parametrization of the Actions of ˆ† (6 ,6,k ;n) 75
  4.5 Conjugacy Classes of the Non-degenerate Homomorphisms 79