- 14

- 0

**1. Homework Statement**

Show that every abelian group of order 70 is cyclic.

**2. Homework 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!

Last edited: