Hi all,

Another problem I am not sure whether I am missing something or not.

Problem:

A finite group $\displaystyle G$ has elements of orders $\displaystyle p$ and $\displaystyle q$, where $\displaystyle p$ and $\displaystyle q$ are distinct primes. What can you conclude about $\displaystyle |G|$?

Solution:

I said that $\displaystyle |G| = kpq$ for some $\displaystyle k \in \mathbb{Z}_{>0} $. As a consequence of Lagrange's Theorem (the orders of the elements must divide |G|)

does that seem like the observation they wanted me to make?

Thanks