*Exercise 3. Let phi :G_(1)->G_(2) be a homomorphism, let H_(2) be a subgroup of G_(2), and let
H_(1)=phi ^(-1)(H_(2))={ginG_(1):phi (g)inH_(2)}.
(a) Prove that H_(1) is a subgroup of G_(1).
(b) Prove that if H_(2) is normal in G_(2), then H_(1) is normal in G_(1).
(Note: since the trivial subgroup is always normal, it follows that kerphi is a normal subgroup
of G_(1).)
*Exercise 3. Let : G1 -> G2 be a homomorphism, let H2 be a subgroup of G2, and let H1=-1(H2)={g E G1:y(g) e H2}.
(a) Prove that H1 is a subgroup of G1.
b) Prove that if H2 is normal in G2,then H is normal in Gi
(Note: since the trivial subgroup is always normal, it follows that ker is a normal subgroup of G1.)
