Epimorphism from G to Z.

[LeviathanTheEsper]

Hello. I've got a problem with this exercise, I'd be thankful if someone could help.
Let G be a group and let f be an epimorphism from G to

. Show that for every positive integer n, G has a normal subgroup of index n in G.
Hint: Define an epimorphism from G in

and use the First Isomorphism Theorem.

 

[HallsofIvy]

What have you done on this? You are taking this course aren't you? Do you know the definitions? What is an "epimorphism"? What is a "normal subgroup"?