Group Homomorphisms Definitions, examples, and proofs talking about group homomorphisms are given. Homomorphisms A homomorphism is a function between two groups. Its a way to compare two groups for structural similarities. Homomorphisms are a powerful tool for...
Permutations In the following video, permutations is introduced, examples and T/F questions are shown. Symmetric Groups Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of...
Definition of a Cyclic Group The definition of a cyclic group is given along with several examples of cyclic groups. Cyclic Subgroups A definition of cyclic subgroups is provided along with a proof that they are, in fact, subgroups. The Structure of...
Learn the definition of a subgroup. The following video describing the definition of a subgroup along with a few examples. In this video, the basics of what it means to be a subgroup explain, and some fun problems working with subgroups are shown. The...
The Order of an Element The order of an element in a group is the smallest positive power of the element which gives you the identity element. We discuss 3 examples: elements of finite order in the real numbers, complex numbers, and a 2×2 rotation matrix. ...
