# Math Help - kernel of an action

1. ## kernel of an action

I proved that $G_b = gG_ag^{-1}$. How to deduce that if $G$ acts transitively on the set $A$, then the kernel of the action is the intersection of $gG_ag^{-1}$ for every $g \in G$

2. Originally Posted by dori1123
How to deduce that if $G$ acts transitively on the set $A$, then the kernel of the action is the intersection of $gG_ag^{-1}$ for every $g \in G$
How do you define kernel of a group action?

3. I've attached a document. Thank you.

4. Can anyone help me with this?