子群 PROOF.We will first show that HN {hn h E H,n E N}is a subgroup of G.Suppose that hin1,h2n2 HN.Since N is normal,(h2)-1n1h2 E N. So (h1n1)(h2n2）=h1h2(h2)-1n1h2)m2 is in HN.The inverse of hn E HN is in HN since (hm)-1=n-1h-1=h-1(hn-1h-1),子群