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.
Also see
- Results about commutativity can be found here.
Sources
- 1978: John S. Rose: A Course on Group Theory ... (previous) ... (next): $0$: Some Conventions and some Basic Facts