Group operation

Notation and terminology

More generally, one speaks of an additive group whenever the group operation is notated as addition; in this case, the identity is typically denoted ⁠${\displaystyle 0}$⁠, and the inverse of an element ${\displaystyle x}$ is denoted ⁠${\displaystyle -x}$⁠. Similarly, one speaks of a multiplicative group whenever the group operation is notated as multiplication; in this case, the identity is typically denoted ⁠${\displaystyle 1}$⁠, and the inverse of an element ${\displaystyle x}$ is denoted ⁠${\displaystyle x^{-1}}$⁠. In a multiplicative group, the operation symbol is usually omitted entirely, so that the operation is denoted by juxtaposition, ${\displaystyle ab}$ instead of ⁠${\displaystyle a\cdot b}$⁠.