# Math Help - Prove Cyclic

1. ## Prove Cyclic

Suppose that G is Abelian group of order 35 and every element of G satisfies the equation x^35=e. Prove that G is cyclic

2. Originally Posted by mandy123
Suppose that G is Abelian group of order 35 and every element of G satisfies the equation x^35=e. Prove that G is cyclic
The condition $x^{35} = e$ is absolutely unnecessary because that is just Lagrange's theorem.
Since $35 = 5\cdot 7$ for two distinct primes it means that is must be cyclic.