Definition:Multiplicative Group

Definition
Let $\struct {F, +, \times}$ be a field.

Let $F^* := F \setminus \set 0$ be the set $F$ less its zero.

The group $\struct {F^*, \times}$ is known as the multiplicative group of $F$.

Also see

 * Multiplicative Group of Field is Abelian Group: by definition of a field, the multiplicative group of a field is abelian.