1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Groups and kernels?

  1. Jan 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Expain why every normal subgroup is the kernel of some homomorphism.

    3. The attempt at a solution
    Every kernel is a normal subgroup but the reverse I can't show rigorously. It seems possible how to show?
  2. jcsd
  3. Jan 13, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    What's the obvious map from G to G/N? What's its kernel?
  4. Jan 13, 2008 #3


    User Avatar
    Science Advisor

    I would have thought that would be easy- it's the direction emphasised in Algebra texts! Of course, this says "some" homomorphism- you have to pick the homomorphism carefully.

    If H is a normal subgroup G, then we can define the "quotient group", G/H. There is an obvious homomorphism from G to H. What is the kernel of that homomorphism?

    Darn, I had to stop in the middle to take a telephone call and morphism got in in front of me!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook