Group Theory

  1. Free Groups and Presentations
    1. Free Groups
      1. Definition of Free Group
        1. Universal Property
          1. Reduced Words
            1. Rank of Free Groups
            2. Generators and Relations
              1. Group Presentations
                1. Defining Relations
                  1. Word Problem
                  2. Examples of Presentations
                    1. Cyclic Groups
                      1. Dihedral Groups
                        1. Free Abelian Groups
                        2. Von Dyck's Theorem
                          1. Statement and Applications
                            1. Quotients of Free Groups
                            2. Tietze Transformations
                              1. Elementary Operations
                                1. Equivalence of Presentations

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                              17. Composition Series and Jordan-Hölder Theorem

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                              19. Semidirect Products