(40) Prove or disprove each of the following. (a) If n = p where p is...

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(40) Prove or disprove each of the following. (a) If n = p² where p is prime, then there are exactly 2 distinct (up to isomorphism) Abelian groups of order n. (b) If n = p³ where p is prime, then there are exactly 3 distinct (up to isomorphism) Abelian groups of order n. (c) If n = pk where p is prime, then there are exactly k distinct (up to isomorphism) Abelian groups of order n. I (40) Prove or disprove each of the following. (a) If n = p² where p is prime, then there are exactly 2 distinct (up to isomorphism) Abelian groups of order n. (b) If n = p³ where p is prime, then there are exactly 3 distinct (up to isomorphism) Abelian groups of order n. (c) If n = pk where p is prime, then there are exactly k distinct (up to isomorphism) Abelian groups of order n. I