Suppose that a is a group element and $a^6 = e$. What are the possibilities for $|a|$? 
Suppose that $a$ is a group element and $a^6 = e$. What are the possibilities for $|a|$? (Gallian, Contemporary Abstract Algebra, Exercise 18, Chapter 3.)

I just started looking at Abstract Algebra again and I was stuck on this question. It will probably be extremely simple for all of you but I didn't know what to do.
I tried doing regular operations like those found in arithmetic but obviously, that is one of the reasons why Abstract Algebra is so difficult.

What does $|a|$ mean?  It is the order of $a$.  This is defined to be

the smallest positive number $n$ for which $a^n = e$.

But you know that $a^6 = e$.  So whatever $|a|$ is, it is a positive number that is not more than 6. That narrows down the possibilities considerably.  Can you proceed from there?
