Abstract
The complete list of pairs of non-isomorphic finite simple groups having the same order is well known. In particular, for p > 3, PSL2(Z/p) is the "only" simple group of order p(3)-p/2. It's less well known that Frobenius proved this uniqueness result in 1902. This note presents a version of Frobenius' argument that might be used in an undergraduate honors algebra course. It also includes a short modern proof, aimed at the same audience, of the much earlier result that PSL2(Z/p) is simple for p > 3, a result stated by Galois in 1832.