I have no clue how to attack these question one. All help or hints is appreciated.

G always denotes a group

1. Let G be finite and G not equal to {e}. Show that G has an element of prime order.

2. Prove that isomorphic groups have isomorphic automorphism groups.

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.

Thanks!