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How many different non-isomorphic Abelian groups of order 16 are there?

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The number of Abelian groups of order  P^k (P is prime) is the number of partitions of  k.

Prime factorization of 16 = 2^4

The partitions of power i.e.., 4 = {1+1+1+1},{2+1+1},{2+2},{3+1},{4}

So total partitions =5

Answer =5

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