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How many different non-isomorphic Abelian groups of order 16 are there?
asked in Set Theory & Algebra by Boss (35.4k points) | 93 views
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Is it 5?
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yes also please explain difference between isomorphic and non-isomorphic abelian groups
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I have encountered one such problem in this link

https://gateoverflow.in/1219/gate2007-21

There is a video attached in the comments about the isomorphism part but I am unable to understand it clearly

1 Answer

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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

answered by Active (2.5k points)

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