Is it correct to say H is normal sub-group of G, IFF (IF AND ONLY IF) G|H is a group?
Thanks,
Aman
one side is probably in your textbook. the other side: if $\displaystyle G/H$ is a group, then $\displaystyle f: G \longrightarrow G/H$ defined by $\displaystyle f(g)=Hg$ is a well-defined group homomorphism and $\displaystyle \ker f = H.$ thus $\displaystyle H \lhd G.$