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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


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    Staff Emeritus
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    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
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