The Structure of the Group F × p

In this chapter we want to introduce, and briefly discuss, another algebraic structure that is a little more abstract, in the sense that we require fewer properties than was the case with rings. As we will see, this will result in even more examples of this structure. Roughly speaking, studying counting and equations led us naturally to the abstract concept of a ring. Studying symmetry (of geometric and algebraic objects) historically led to the concept of a group.