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: Isomorphic quotient groups

  1. Feb 4, 2008 #1
    1. The problem statement, all variables and given/known data
    Let H and K be normal subgroups of a group G. Give an example showing that we may have H isomorphic to K while G/H is not isomorphic to G/K.

    2. Relevant equations

    3. The attempt at a solution
    I don't want to look in the back of my book just yet. Can someone give me a hint?
  2. jcsd
  3. Feb 4, 2008 #2


    User Avatar
    Homework Helper

    If G and K are conjugates, then its easy to show that G/H and G/K are isomorphic, so you need to look for non-conjugate subgroups (more generally, this is true if there is an automorphism of G taking H to K). You also obviously need to pick [G:H] so that there is actually more than one group of this order.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook