Definition:Permutable Subgroups

Definition
Let $$G$$ be a group.

Let $$H$$ and $$K$$ be subgroups of $$G$$.

Let $$HK$$ denote the subset product of $$H$$ and $$K$$.

Then $$H$$ and $$K$$ are permutable iff $$HK = KH$$.

Also see
From Subset Product of Subgroups, we have that $$HK$$ is itself a subgroup of $$G$$ iff $$H$$ and $$K$$ are permutable.