同构 Now define a map o from H to HN/N by h hN.The map o is onto, since any coset hnN hN is the image of h in H.We also know that o is a homomorphism because (hh')=hh'N hNh'N =(h)o(h'). By the First Isomorphism Theorem,the image of o is isomorphic to H/ker that is, HN/N=(H)≌H/kero. Since kero={h∈H:heN}=HnN, HN/N=(H)兰H/H∩N. 0同构