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3. Suppose G = <a> is a cyclic group of order 15 (i.e. a has order...

3. Suppose G = <a> is a cyclic group of order 15 (i.e. a has order 15), and consider the subgroup K = <a^3>.

(a) Determine the order of K.

(b) Use Lagrange’s theorem to determine the index of K in G, and then list the distinct cosets of K in G explicitly. (Hint: Consider the cosets Ke and Kb for b does not ∈K

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