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## Homework Statement

If G is a finite abelian group that has one subgroup of order d for every divisor d of the order of G. Prove that G is cyclic.

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- Thread starter curiousmuch
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If G is a finite abelian group that has one subgroup of order d for every divisor d of the order of G. Prove that G is cyclic.

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quantumdude

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Post what you've done on this problem please.

- #3

matt grime

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Can you check the question. C_2 x C_2 has subgroups of orders 1,2 and 4, but is not cyclic.

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Dick

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Can you check the question. C_2 x C_2 has subgroups of orders 1,2 and 4, but is not cyclic.

I think the point is that it is supposed to have ONE subgroup of each order. Your example has several subgroups of order 2.

- #5

matt grime

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And that's why we have the word 'exactly'.

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