
#1
May709, 08:59 AM

P: 9

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 



#2
May709, 02:56 PM

Emeritus
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PF Gold
P: 5,540

Post what you've done on this problem please.




#3
May709, 03:31 PM

Sci Advisor
HW Helper
P: 9,398

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




#4
May709, 03:58 PM

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HW Helper
Thanks
P: 25,174

Proving converse of fundamental theorem of cyclic groups 



#5
May809, 01:12 AM

Sci Advisor
HW Helper
P: 9,398

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



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