Understanding Stabilizers in Quotient Groups | G/H Coset Stabilizers Explained

[SNOOTCHIEBOOCHEE]

Homework Statement

What is the stabilizer of the coset aH for the operation of G on G/H

The Attempt at a Solution

Its hard for me to do this because i don't really understand the problem. i know that the stabalizer of an ELEMENT s in some group is the subgroup G_s = {g element of G|gs=s}

so basically its all elements of G that act as the identity. but i don't know how to apply this to quotient groups.

 

[Office_Shredder]

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