Consider a [group](Groups.md) $\mathrm{G}.$ The _induced operation_ refers to the group operation applied to a [subset](Sets.md#Subsets) of that group, $\mathrm{H}$. The induced operation [maps](Maps.md) pairs of ordered elements in that subset to the same element as it does when the same operation is applied in the whole group. #MathematicalFoundations/Algebra/AbstractAlgebra