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:

$H \circ K = K \circ H$

Also see

• Subset Product of Subgroups: $H \circ K$ is itself a subgroup of $G$ if and only if $H$ and $K$ are permutable.

Sources

• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $5$: Cosets and Lagrange's Theorem: Proposition $5.17$