Hi: Let G be a group and N normal in G such that 1 and N are the only normal subgroups of G that are contained in N. Let be a surjective (onto) homomorphism from G to a group H. Let be a normal subgroup of that is contained in and let . Then is normal in .
OK. But I am said that, then, since . I have been trying hard to prove that but I could not. Any suggestion?
Notation: 1 stands for the trivial subgroup of G.