This is what I have so far:If N is a finite normal subgroup of a group G and if G/N contains an element of order n, prove that G contains an element of order n.
Let have order n for some . Then , so . Since N is finite, let . Then , so .
When I pursued this line of reasoning, I was trying to show that , and thus . However, I'm stuck here. Have I made a mistake somewhere, or am I missing something?
Thanks for any insights.