1. The problem statement, all variables and given/known data Show that every abelian group of order 70 is cyclic. 2. Relevant equations Cannot use the Fundamental Theorem of Finite Abelian Groups. 3. 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!