In an undergrad honors algebra course it's sometimes shown that when p is prime and >3 then PSL_2(Z/p) is simple of of order p(p-1)(p+1)/2. But that this is the "only" simple group having that order is seldom or never (except when p=5) proved.

I've worked out a fairly simple proof, using the Burnside transfer theorem, of this last result, but it's perhaps a little too intricate to present in class.

QUESTION: Are there proofs of this result, on-line or in texts, that are appropriate for an undergrad honors algebra class? (If not, I might post an argument on arXiv).