Definition:Multiplicative Group

Definition
Let $\left({F, +, \times}\right)$ be a field.

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

The group $\left({F^*, \times}\right)$ 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.