Definition:Multiplicative Notation

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Multiplicative notation, also called product notation, is a convention for representing a binary operation of an algebraic structure.

Let $S$ be such an algebraic structure, and let $x, y \in S$.

$x y$ is used to indicate the result of the operation on $x$ and $y$. There is no symbol used to define the operation itself.
$e$ or $1$ is used for the identity element.
$x^{-1}$ is used for the inverse element.
$x^n$ is used to indicate the $n$th power of $x$.

This notation is usual in group theory when discussing the general group.

It is also the usual notation in:

ring theory for the ring product
field theory for the field product.

Also see