Page 113 - Dummit and Foote - Group actions
Two group elements induce the same permutation on $A$ if and only if they are in the same coset of the kernel.
What does this mean? Two permutations induce the same permutation on $A$ looks like it means $\sigma_1 A = A' = \sigma_2 A$ and then I don't really understand the right hand side of the $\iff$.