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.)
Abelian Groups of order 2000
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group-theory
abelian-groups
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0sorry, I changed the title. – 2012-11-14
1 Answers
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$2,000=2^4\cdot 5^3$
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:
$C_{2,000}\;,\;C_{16}\times C_{25}\times C_5\;,\;C_8\times C_2\times C_5\times C_5\ \times C_5\;,\;etc.$
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0I 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. – 2012-11-14