chapter  8
20 Pages

Groups

Let’s denote the set by G and the operation by ★. By operation we understand a rule for combining any two elements a and b of G to get another element of G, which we denote by a ★ b.

It is often the case in mathematics that a set comes equipped with an opera­ tion. Familiar examples include the natural numbers with addition, the integers with addition, the rational numbers with multiplication, and vectors in 3-space with the vector product.