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: 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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook