| LIST OF THEOREMS LIST OF ADOPTED CONVENTIONS Ⅰ. INTEGRAL FUNCTION 1. Interpolation 2. Division 3. Reduction 4. Primitive function 5. Linear factors Ⅱ. EQUATIONS AND PERMUTATIONS 6. Discovery of Lagrange 7. Solution of cubic 8. Connection with permutations Ⅲ. ALGEBRA OF PERMUTATIONS 9. Notation 10. Degree 11. Combination 12. Order 13. Association 14. Inverse 15. Identity Ⅳ. GROUP AND SUBGROUP 16. Group 17. Subgroup 18. Conjugate subgroups 19. Rule of transforms 20. Normal subgroup Ⅴ. SYMMETRIC GROUP AND ITS FUNCTIONS 21. Generator 22. Symmetric sum 23. Computation of symmetric sum 24. Another computation 25. Resultant 26. Resultant as determinant 27. Discriminant Ⅵ. COMPOSITION OF SYMMETRIC GROUP 28. Composition-series 29. Alternating function 30. Alternating group 31. Composition of S and A 32. Subgroups of S and A 33. Group on functions Ⅶ. THEORY OF LAGRANGE 34. Resolvent equation 35. Lagrange's Theorem 36. Lagrange's Theorem, Continued 37. Plan of Lagrange 38. Lagrange's solvent 39. Special case of solvents 40. Limits of Lagrange's plan Ⅷ. GENERAL EQUATIONS 41. Quadratic equation 42. Cubic equation 43. Cubic equation, Continued 44. Cubic equation, Continued 45. Cubic equation, Continued 46. Biquadratie equation 47. Biquadratic equation, Continv, ed 48. Biquadratic equation, Continued Ⅸ. MORE ABOUT GROUPS 49. Isomorphic groups 50. Transitive group 51. Imprimitive group 52. Quotient-group 53. Subgroups of quotient-group 54. Maximum normal subgroup 55. Constancy of composition-factors 56. Abelian group 57. Theorem of Cauchy 58. Metacyclic group Note on abst group Ⅹ. DOMAIN 59. Algebraic domain 60. Algebraic domain, Continued. 61. Coniugate domains 62. Conjugate domains, Continued 63. Normal domain Ⅺ. THEORY OF GALOIS 64. Special equation 65. Galoisian function 66. Galoisian resolvent 67. Galoisian group 68. Properties of Galoisian group …… Ⅻ. SPECIAL EQUATIONS INDEX |
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