Definition:Permutable Subgroups

Definition
Let $\left({G, \circ}\right)$ 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 $H \circ K = K \circ H$.

Also see

 * Subset Product of Subgroups: $H \circ K$ is itself a subgroup of $G$ iff $H$ and $K$ are permutable.