Let h be a normal subgroup of g, and let G/HHgIgEG ◆ For VHg1 and Hg2∈G/H, ◆ Let Hg oHg2=H(g1*g2 Lemma 3: Let H be a normal subgroup of G. Then G/H; e is a algebraic system a+ Proof: is a binary operation on G/H ◆ For VHg1=Hg3 and Hg2=Hg4∈G/H, ◆Hg1②Hg2=H(g12g2),Hg3SHg=H(g32g4) ◆Hg1Hg2=Hg3Hg? ◆H(g1*g2)=2H(g3g4 ?H(g g2),le (g3*g4)*(g1g2)∈?H Let H be a normal subgroup of G, and let G/H={Hg|gG}  For Hg1 and Hg2G/H,  Let Hg1Hg2=H(g1*g2 )  Lemma 3: Let H be a normal subgroup of G. Then [G/H; ] is a algebraic system.  Proof:  is a binary operation on G/H.  For Hg1=Hg3 and Hg2=Hg4G/H,  Hg1Hg2=H(g1*g2 ), Hg3Hg4=H(g3*g4 ),  Hg1Hg2?=Hg3Hg4?  H(g1*g2 )=?H(g3*g4 )  g3*g4?H(g1*g2 ), i.e. (g3g4 )(g1*g2 ) -1?H