# Math Help - Isotropy Group and equivalent relation

1. ## Isotropy Group and equivalent relation

Hello,

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, $f:G x A->A$ a group action and $G_a$ the isotropy group of a $\in A$.

Now my professor has denoted followin equiv. relation on G:

g ~ g'<=>ga=g'a<=>g'^(-1)g=g^(-1)g' $\in G_a <=> g=g'mod G_a$=>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.

Thank you.

2. It says that $G_a$, the isotropy group of a, is isomorphic to the quotient group $G/G_a$. Have you dealt with quotient groups?

3. Oh yes, thank you for your help.

Yes i know the Quotient Group. Now i'm clear in that point.

thanks a lot.