Let p be a prime number. How many Abelian groups (up to isomorphism) are there of order p^100.

I am stuck, Please Help(Crying)

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- November 16th 2008, 03:27 PMmandy123How many Abelian groups are there
Let p be a prime number. How many Abelian groups (up to isomorphism) are there of order p^100.

I am stuck, Please Help(Crying) - November 16th 2008, 03:33 PMThePerfectHacker
- November 16th 2008, 03:50 PMmandy123
I don't have a more general problem, this is all I am given. Is that bad?

So if I follow what you did, would there be 100 Abelian groups? - November 16th 2008, 04:08 PMJhevon
- November 16th 2008, 04:16 PMThePerfectHacker
- November 16th 2008, 04:16 PMNonCommAlg
by the fundamental theorem of finite abelian groups, the answer is the number of partitions of 100, which according to this website is equal to 190569292.

- November 16th 2008, 04:20 PMJhevon
- November 16th 2008, 04:21 PMJhevon
- November 16th 2008, 04:25 PMThePerfectHacker
I do not think there is a partitions formula.

The # of partitions is a very complicated combinatorics problem.

There are ways to get them using recurrence relations and all that stuff. But as far as a formula that give you an answer it is does not exist. At least I never seen one. (Worried). I am scared!