Please bear with me as I don't have latex. This is a homework question I have and I don't even know if it makes sense: How many Z_3 (set of integers modulo 3) vector space automorphisms of Z_3(alpha) are there? Describe them. I'm not sure if alpha is supposed to be the root of some polynomial or just an element outside of Z_3. I know that Z_3 is isomorphic to GF(3) (the Galois field of order 3). Any help would be much appreciated.