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Consider the set S = {1, ω, ω²}, where ω and ω² are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms

1. a group
2. a ring
3. an integral domain
4. a field

Correct answer: a group

Solution

The set S = {1, ω, ω²} with multiplication satisfies the group properties: it is closed under multiplication, has an identity element (1), and every element has an inverse (1, ω, and ω² are all roots of unity). Thus, it forms a group.

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