Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Classify, up to isomorphism, all abelian groups of order 2,000, giving the standard form of each group in your list. (The standard form is also called the invariant factor decomposition.)

share|improve this question
8  
Eer....where in your question do characters appear?? –  DonAntonio Oct 31 '12 at 22:31
    
sorry, I changed the title. –  neno Nov 14 '12 at 17:47
add comment

1 Answer 1

up vote 6 down vote accepted

$$2,000=2^4\cdot 5^3$$

Now, the number of partitions of $\,4\,$ is $\,5\,$, and the number of partitions of $\,3\,$ is $\,3\,$ , so the number of different abelian groups of order $\,2,000\,$ up to isomorphism is $\,5\cdot 3=15\,$ .

Some of them are:

$$C_{2,000}\;,\;C_{16}\times C_{25}\times C_5\;,\;C_8\times C_2\times C_5\times C_5\ \times C_5\;,\;etc.$$

share|improve this answer
    
Can I use Zn instead of Cn? –  neno Nov 14 '12 at 17:43
    
I think so, but this can be a nuisance as the group operation changes to addition. But if you're more used to this no problem. –  DonAntonio Nov 14 '12 at 18:42
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.