Students will learn what the center of a group is. After knowing the definition for the center of a group, it should be apparent that the center of any abelian group is the group itself. Students will also see that sometimes the center is the entire group, for example, \(\mathbb{Z}_4,\) sometimes the center is just the identity element, example, \(\mathbb{S}_3,\) and sometimes the center is neither just the identity, nor the entire group. For example, \(D_4.\) Finally, students will learn why the center of a group \(G\) is a subgroup of \(G.\) Here's an excellent demonstration on all that.
