Group Theory

  1. Solvable and Nilpotent Groups
    1. Commutator Subgroups
      1. Definition of Commutator
        1. Derived Subgroup
          1. Properties of Derived Subgroups
          2. Solvable Groups
            1. Definition of Solvable Group
              1. Derived Series
                1. Solvable Length
                  1. Examples of Solvable Groups
                    1. Properties of Solvable Groups
                    2. Nilpotent Groups
                      1. Definition of Nilpotent Group
                        1. Lower Central Series
                          1. Upper Central Series
                            1. Nilpotency Class
                              1. Examples of Nilpotent Groups
                                1. Properties of Nilpotent Groups
                                2. Relationships
                                  1. Nilpotent Implies Solvable
                                    1. p-Groups are Nilpotent
                                      1. Finite Nilpotent Groups

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                                    15. Structure of Finite Abelian Groups

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                                    17. Composition Series and Jordan-Hölder Theorem