I am reading the proof of the fact that as a group under multiplication, the set of nonzero elements of (the Galois field/finite field of order ) is isomorphic to and is therefore cyclic.
During the course of the proof, the author reminds the reader that the operation is componentwise addition. I do not see why this is true...we are looking at the multiplicative group of the field. Can someone explain? (I will add more detail if necessary).