Question

(a) Validate whether an underlying set S = 3Z = {3n: n ∈ Z}, the set of integers that are
multiples of 3 with an operation * is + , indeed an abelian a group.

Answer 1

Answer:

Define 3Z as the set of integer multiples of 3: Recall the simpler subgroup criterion from today: Let G be a group with subset H H is a subgroup of G if and only if H is nonempty and for all a, b e H, we have ab e H Use the subgroup criterion above to prove that (3Z, +)s (Z, +). (Note: Since the group operation is addition here, "ab" would mean a(-b), .e. a b.)