1. May 7, 2009 #1

   curiousmuch

   

   1. The problem statement, all variables and given/known data
   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.
   
   
   2. Relevant equations
   
   
   
   3. The attempt at a solution

    

   curiousmuch, May 7, 2009
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3. May 7, 2009 #2

   Tom Mattson

   

   Staff Emeritus

   Science Advisor

   Gold Member

   Post what you've done on this problem please.

    

   Tom Mattson, May 7, 2009
4. May 7, 2009 #3

   matt grime

   

   Science Advisor

   Homework Helper

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

    

   matt grime, May 7, 2009
5. May 7, 2009 #4

   Dick

   

   Science Advisor

   Homework Helper

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

    

   Dick, May 7, 2009
6. May 8, 2009 #5

   matt grime

   

   Science Advisor

   Homework Helper

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

    

   matt grime, May 8, 2009

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