Theorem 10.2 Let N be a normal subgroup of a group G.The cosets of N in G form a group G/N of order G:N. PROOF.The group operation on G/N is (aN)(bN)=abN.This operation must be shown to be well-defined;that is,group multiplication must be independent of the choice of coset representative.Let aN =bN and cN dN.We must show that 、证 有 (aN)(cN)=acN bdN =(bN)(dN). Then a=bni and c=dn2 for some n and n2 in N.Hence, acN =bnidn2N =bnadN =bniNd bNd bdN.我们必须保证 这个定义是有 效的！