Question

(a) Prove that any finite group is a subgroup of 6 a permutation group.

(b) Let d be a Euclidean norm on a Euclidean domain D. Show that if sEZ such that s + d(1)>O, then g : D\ (0}—>Z g(a) = d(a) + s, for non-zero aED, is a Euclidean norm on D.