A study of permutation groups and coherent configurations
نویسندگان
چکیده
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii CHAPTER 1. HISTORICAL BACKGROUND . . . . . . . . . . . . . . . . . 1 1.1 Early Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Resolvent Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 More Recent Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.1 Galois Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.2 Additional Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 CHAPTER 2. SHARPLY 2-TRANSITIVE GROUPS . . . . . . . . . . . . . 6 2.1 Notation and Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Coset Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Characterization of Sharply 2-Transitive Permutation Groups . . . . . . . . . . 12 CHAPTER 3. COHERENT CONFIGURATIONS . . . . . . . . . . . . . . . 18 3.1 Coherent Configurations and Basis Algebras . . . . . . . . . . . . . . . . . . . . 18 3.2 Association Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Schur Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.4 Construction of Non-Symmetric Commutative Association Schemes Using Schur Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.5 Permutation Representations and Centralizer Algebras . . . . . . . . . . . . . . 30 3.6 Character Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
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Coherent configurations, association schemes and permutation groups
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