Call
In mathematics, one can define a product of group subsets in a natural way. If S and T are subsets of a group G, then their product is the subset of G defined by
The subsets S and T need not be subgroups for this product to be well defined. The associativity of this product follows from that of the group product. The product of group subsets therefore defines a natural monoid structure on the power set of G.
A lot more can be said in the case where S and T are subgroups. The product of two subgroups S and T of a group G is itself a subgroup of G if and only if ST = TS.