Double transversal of a subgroup

Definition with symbols
Let $$H$$ be a subgroup of a group $$G$$. Then a subset $$S$$ of $$G$$ is termed a double transversal of $$H$$ in $$G$$ if $$S$$ intersects every double coset of $$H$$ at exactly one element.

$$S$$ is also termed a system of double coset representatives of $$H$$ and the elements of $$S$$ are termed double coset representatives of $$H$$.