Can You Multiply Cosets?

Coset multiplication is well-defined on the set G/H of left cosets ⇐⇒ for all g ∈ G, the right coset Hg is contained in the left coset gH. ... This says that the left coset gH is contained in the right coset Hg. Thus, if Hg ⊆ gH holds for all g ∈ G, then gH ⊆ Hg for all g ∈ G as well, and hence Hg = gH.

Can a coset be a group?

Cosets of a particular type of subgroup (a normal subgroup) can be used as the elements of another group called a quotient group or factor group.

How many distinct Cosets are there?

So there are 4 distinct cosets.