# Definition:Permutable Subgroups

## Definition

Let $\struct {G, \circ}$ be a group.

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

Let $H \circ K$ denote the subset product of $H$ and $K$.

Then $H$ and $K$ are permutable if and only if:

$H \circ K = K \circ H$