Group Theory

  1. Direct Products and Sums
    1. External Direct Product
      1. Definition and Construction
        1. Properties of External Direct Products
          1. Order of Elements in Direct Products
            1. Subgroups of Direct Products
            2. Internal Direct Product
              1. Definition and Conditions
                1. Recognition Theorem
                  1. Relationship to External Direct Product
                  2. Direct Sum of Abelian Groups
                    1. Definition for Abelian Groups
                      1. Relationship to Direct Product
                        1. Infinite Direct Sums
                        2. Decomposition Theorems
                          1. Unique Factorization
                            1. Indecomposable Groups

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                          13. The Sylow Theorems

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                          15. Structure of Finite Abelian Groups