Okay, given a function for a group action of the group G acting on a set A (with a fixed point a of A): $\displaystyle \phi _a : G \times \{ a \} \to A$. One definition I have for the kernal is $\displaystyle ker \phi _a = \{ (g, a) | \phi _a (g, a) = 1_A ~ \forall g \in G \}$. But the definition in the group action section is that $\displaystyle ker \phi _a = \{ g \in G | g \cdot a = a \}$. Are these somehow equivalent? I don't see it.

-Dan