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How many different non-isomorphic Abelian groups of order 16 are there?
in Set Theory & Algebra 308 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

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@Bhagyashree Mukherje 

@Mk Utkarsh

1)If we want non-isomorphic and non-abelian group, then what will be ans??

2) If we want isomorphic group of order 16, then what will be ans??

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

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