Is G/H Always an Abelian Group if H is Normal in G?

[Kanchana]

Let H be a normal subgroup of G. Then factor group G/H is an abelian subgroup.
For x, y not in H
xHyH=yHxH
and xyH=yxH
(xyH)(yxH)^{-1}=id
xyx^{-1}y^{-1}=id

Are these steps correct?


thnx

 

[micromass]

Let H be a normal subgroup of G. Then factor group G/H is an abelian subgroup

Are you trying to prove this?

What happens if $H=\{e\}$?

Also, the factor group $G/H$ is not a subgroup of $G$.