# Definition:Commutative/Set

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## Definition

Let $\struct {S, \circ}$ be an algebraic structure.

Let $X \subseteq S$ be a subset of $S$ such that:

$\forall a, b \in X: a \circ b = b \circ a$

That is, every element of $X$ commutes with every other element.

Then $X$ is a commuting set of elements of $S$.

## Also defined as

Some treatments use this definition only when the algebraic structure $S$ is a group.

## Also known as

The terms permute and permutable can sometimes be seen instead of commute and commutative.