Group Theory

  1. Introduction to Representation Theory
    1. Linear Representations
      1. Definition of Group Representation
        1. Matrix Representations
          1. Degree of Representation
            1. Equivalent Representations
            2. Examples of Representations
              1. Trivial Representation
                1. Regular Representation
                  1. Permutation Representations
                  2. Characters
                    1. Definition of Character
                      1. Character Tables
                        1. Orthogonality Relations
                        2. Irreducible Representations
                          1. Definition and Examples
                            1. Schur's Lemma
                              1. Complete Reducibility
                              2. Applications
                                1. Burnside's Theorem
                                  1. Representation Theory of Finite Groups

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                                19. Semidirect Products

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                                21. Applications of Group Theory