[r-t] algebraic theory

[Robin Woolley]

Hi All,

I am thinking here about the groups S5 and A5.

I believe that given any two elements p and q, then the orders of p and q 
divide the order of the (finite) group. (A brief scan of the literature 
fails to explcitly confirm this).

Question: Is there an easy way of deciding the maximum order of an element 
in a finite group - I believe that for S5 this equals 6?

Question: Since pq is in the group also, what is the order of pq? (i.e., if 
ord(p) = 2 and ord(q) = 4, then is it easy to write down ord(pq)? - I don't 
think it can be eight, for instance).

Thanks in anticipation
Robin