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.