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Proving converse of fundamental theorem of cyclic groups

  • #1

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.


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Tom Mattson
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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.
 
  • #4
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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