A group whose group operation is identified with multiplication. As with normal multiplication, the multiplication operation on group elements is either denoted by a raised dot · or omitted entirely, giving the notation g·h or g h. In a multiplicative group, the identity element is denoted 1, and the inverse of the element g is written as g^(-1), voiced "g inverse." This notation and terminology is borrowed from the multiplicative groups formed by numbers, where the operation is the usual arithmetical product, the identity element is the number 1, and the inverse coincides with the multiplicative reciprocal.

additive group | multiplication | multiplication table | multiplicative inverse | quaternion group