Group Theory

  1. Subgroups
    1. Definition of a Subgroup
      1. Subgroup Tests
        1. One-Step Subgroup Test
          1. Two-Step Subgroup Test
            1. Finite Subgroup Test
              1. Non-empty Finite Subset Test
              2. Examples of Subgroups
                1. Subgroups of ℤ
                  1. Subgroups of Symmetric Groups
                    1. Subgroups of Matrix Groups
                      1. Subgroups of Cyclic Groups
                      2. Trivial and Proper Subgroups
                        1. Trivial Subgroup
                          1. Proper Subgroup
                            1. Maximal Subgroups
                            2. Generated Subgroups
                              1. Subgroup Generated by an Element
                                1. Subgroup Generated by a Set
                                  1. Cyclic Subgroups
                                  2. Special Subgroups
                                    1. Center of a Group
                                      1. Definition and Properties
                                        1. Computing Centers
                                        2. Centralizer of an Element
                                          1. Definition and Properties
                                            1. Relationship to Center
                                            2. Centralizer of a Subgroup
                                              1. Normalizer of a Subgroup
                                                1. Definition and Properties
                                                  1. Relationship to Conjugation

                                              Previous

                                              4. Order of Elements and Groups

                                              Go to top

                                              Next

                                              6. Cyclic Groups