{a} is a set with a as the element; H is another set; {a} h juxtaposes two sets to represent one set, but its definition also depends on another object: group.

Firstly, the definition of the product of any two non-empty subsets in a group is given: A and B are non-empty subsets of G; And say:

AB = {a * b | a ∈ A and b ∈ b};

Is the product of a and b;

Then, the special product of {a} h is defined: here, a ∈ g; Yes subgroup; According to the definition of products, there are:

{ a } H = { a * x | x∈H }；

This set is called: the left coset of H in G determined by A; Correspondingly, the right coset can also be defined as: h {a }；; Like the left coset and the right coset, these two sets have special symbols:

aH = { a } H；

ha = H { a }；