Symmetric inverse semigroup

In abstract algebra, the set of all partial bijections on a set X (a.k.a. one-to-one partial transformations) forms an inverse semigroup, called the symmetric inverse semigroup (actually a monoid) on X. The conventional notation for the symmetric inverse semigroup on a set X is ${\displaystyle {\mathcal {I}}_{X}}$ or ${\displaystyle {\mathcal {IS}}_{X}}$ In general ${\displaystyle {\mathcal {I}}_{X}}$ is not commutative.

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