# Multicoset for a tuple of subgroups

Let $G$ be a group and $H_1,H_2,\ldots,H_r$ be an $r$-tuple of subgroups of $G$. Consider the natural action of $G$ on the coset space $G/H_1 \times G/H_2 \times \ldots G/H_r$. The orbits under this action are termed the multicosets for the tuple of subgroups.
Multicoset generalizes the notion of left coset and the more general notion of double coset, to a tuple of $r$ subgroups for $r > 2$.