It says that , the isotropy group of a, is isomorphic to the quotient group . Have you dealt with quotient groups?
my english is not so good, but i try my best to explain my problems to you.
I have a problem with following situation:
Let G be a group, A a arbitrary set, a group action and the isotropy group of a .
Now my professor has denoted followin equiv. relation on G:
g ~ g'<=>ga=g'a<=>g'^(-1)g=g^(-1)g' =>Ga~G/G_a
And my question is, what does Ga~G/G_a means? i never had seen this before.
I hope you can understand my problem. If not, please tell me which part you dont understand.