**COSET**

For H is a
subgroup of group G, and an element a belongs to G.

Than,

aH = { ah :
h ∈ H} is
called

**Left Coset**of H in G generated by a.
Ha = { ha :
h ∈ H} is
called

**Right Coset**of H in G generated by a.
Here,

Ha and aH are both subsets of G.

If e is an identity element, than

He = H = eH .

So in above line H itself is a right or left coset

If group is

**Abelian,**
Than,

ha = ah, ∀ h ∈ H.

**FACTOR OR QUOTIENT GROUP**

Factor or quotient group is a type of group which is created by the multiplication of all the left coset of a group G.

Multiplication of all left coset of G creates a new set of left coset of G.

Shown as, (aH) (bH) = (ab) H

Here ‘

**and ‘***aH’***are left coset and ‘***bH’***‘ is known as Factor or Quotients group.***(ab)H***SEE ALSO:**