Math Help - proofs

1. proofs

I need help solving these proofs:

Let G have order 4. Either G is cyclic, or every element of G is its own inverse. Conclude (but explain why) that every group of order 4 is abelian.

If G has an element of order p and an element of order q, where p and q are distinct primes, then the order of G is a multiple of pq.

2. Originally Posted by steph615
I need help solving these proofs:

Let G have order 4. Either G is cyclic, or every element of G is its own inverse. Conclude (but explain why) that every group of order 4 is abelian.
If G is cyclic then you are done. Cyclic groups are easily proven to be abelian.

If G is not cyclic, then every element is its own inverse. So then $ba = (ba)^{-1} = a^{-1}b^{-1} = ab$.

I'll let you formalize these statements in to a proof.

-Dan