Abstract
We survey the history of Graham Higman’s PORC conjecture concerning the form of the function f(p n) enumerating the number of groups of order p n. The conjecture is that for a fixed n there is a finite set of polynomials in p, g 1(p), g 2(p),…,g k (p), and a positive integer N, such that for each prime p, f(p n)=g i (p) for some i (1≤i≤k) with the choice of i depending on the residue class of p modulo N. We describe some properties of a group recently discovered by Marcus du Sautoy which has major implications for the PORC conjecture.
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