Introduction to Groups

In this chapter, we define the concept of a group. Our examples of groups are mostly, but not always, the set of all symmetries of a given figure. We learn the first important properties of groups and how we can “generate” a group by using only a few elements. We thus answer questions like: How do I get all other isometries of a figure from a few? Then we study the groups generated by one element. We look a little more closely at all the symmetries of the tetrahedron towards the end of this chapter.