3)What is this supposed to mean?
This is not true just consider then .b)If G is of finite order n then prove that the group of automorphisms of G (i.e.AutG) is isomorphic to the group of those positive integers <n, which are co-prime to n, with binary operation as multiplication modulo n and order of Aut(G)=phi(n)(phi is Euler's phi function).
I assume you mean .Aut(Zn,+n)is isomorphic to (Zncross,cross)
To prove this note if is an isomorphism it is completely determined by .
Now find the conditions to where can get mapped to.
It turn out it is where as the only possible ones.
Then it is easy to show that the automorphism group is
c)Construct an abelian group G of order 27 in which x3 = 1 for all x in G.