Coset

If G is a group and H a subgroup of G, x is an element in G, and h is an element in H the cosets of H in G are defined as follows: 

Left coset: xH is the set of all the elements h of H multiplied by x on the left. 
Right coset: Hx is the set of all the elements h of H multiplied by x on the right. 

When xH = Hx we say that H is normal in G.

Category:Abstract algebra