2. For both parts below, let p :G → G' be a group homomorphism. Let H' be a subgroup of G'. Show that the set H = {g € G| p(g) € H'} is a (a) subgroup of G. (b) elH: H → for all h e H. Show that ker(9) = ker(4|). Hint: Show ker(4) c ker(4|,) and ker(4) Ɔ ker(9|4). Let H a subgroup of G containing ker(9). Define the homomorphism G' by yH = 4OL where i: H → G is the inclusion homomorphism t(h)

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