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redone632
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Homework Statement
Show that every abelian group of order 70 is cyclic.
Homework Equations
Cannot use the Fundamental Theorem of Finite Abelian Groups.
The Attempt at a Solution
I've tried to prove the contrapositive and suppose that it is not cyclic then it cannot be abelian. But that has lead no where quickly.
Something tells me that I need to use the fact that 2*5*7 = 70 and 2 5 7 are all primes. But nothing is clicking. We haven't done the Fundamental Theorem of Finite Abelian Groups so there must be a way to prove this without it. If someone can point me in the right direction that would help a lot!
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