Let and construct . Let . The integer has a prime divisor . The element has order .

Let be a group isomorphism.2. Prove that isomorphic groups have isomorphic automorphism groups.

Define by .

Show this is an isomorphism.

Notice that is a subgroup of and . By Lagrange's theorem it means divides and . Therefore, .3. Let a, b be in G . If |a| and |b| are relatively prime (i.e. gcd (|a|, |b|)=1), then <a> intersection <b> ={e}. Prove the last statement.