Please help me with my assignment in abstract algebra.

1. Show that if E is normal in H, then f-1(E) is normal in G.

2. If G is cyclic, then f(G) is also cyclic.

Hint: G = <a>. Show: f(G)=< f(a)>.

3. I G is a cyclic group of infinite order then G is isomorphic to the additive group 2. Hint: f: G→Z by f(a^m) = m.