Multicoset for a tuple of subgroups

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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.