正规子群的同态保持证明 (4)Let H2 be a subgroup of G2 and define H1 to be(H2);that is, H1 is the set of all gGi such that o(g)EH2.The identity is in H1 since (e)=e.If a and b are in H1,then (ab-1)=(a)[o(b)]-1 is in H2 since H2 is a subgroup of G2.Therefore,ab-1E H1 and H1 is a subgroup of G1.If H2 is normal in G2,we must show that g-1hg∈H1forh∈H1andg∈Gi. But p(g1hg)=[(g)川-1p(h)p(g)∈H2, since H2 is a normal subgroup of G2.Therefore,ghg E H1. 口正规子群的同态保持证明