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!

Stabilizers of cosets

  1. Dec 2, 2008 #1
    1. The problem statement, all variables and given/known data
    What is the stabilizer of the coset aH for the operation of G on G/H



    3. The attempt at a solution

    Its hard for me to do this because i dont really understand the problem. i know that the stabalizer of an ELEMENT s in some group is the subgroup Gs = {g element of G|gs=s}

    so basically its all elements of G that act as the identity. but i dont know how to apply this to quotient groups.
     
  2. jcsd
  3. Dec 3, 2008 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    G/H (the set of cosets) is being acted on by G via the group action

    g*(aH) = (g*a)H

    So you need to find all the g such that (g*a)H = aH
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Stabilizers of cosets
  1. Set of cosets (Replies: 10)

  2. Cosets of Subgroups (Replies: 1)

  3. Right Cosets (Replies: 5)

  4. Coset Question (Replies: 12)

Loading...