1. Not finding help here? Sign up for a free 30min 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!

Subgroups and normal subgroups

  1. Jan 19, 2009 #1
    Let G be a group, let N be normal in G and let H be a subgroup of G. Assume that G/N and H are finite and that gcd(|G/N|,|H|)=1. Prove that H is a subgroup of N.

    I was thinking about using Lagrange Theorem. and maybe using the fact that G may act on the set of left cosets (G/N) by conjugation.
    and the find the kernel of that action and then maybe use the first isomorphism theorem.

    But I don't get very far with that.
  2. jcsd
  3. Jan 19, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    H also acts on G/N by left multiplication. Furthermore, every element of H is in one of the the left cosets of N.
  4. Jan 19, 2009 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Maybe looking at G isn't the right way to go. What can you learn about H by studying the group G/N? What about N?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Subgroups and normal subgroups
  1. Normal Subgroups (Replies: 1)

  2. Normal Subgroups (Replies: 1)

  3. Normal Subgroups (Replies: 2)

  4. Normal subgroup (Replies: 2)