ON GRAHAM HIGMAN''S FAMOUS PORC PAPER

Abstract. we investigate graham higman's paper enumerating p-groups, ii, in which he formulatedhis famous porc conjecture. we are able to simplify some of the theory. in particular, higman'spaper contains five pages of homological algebra which he uses in his proof that the number of solutionsin a finite field to a finite set of monomial equations is porc. it turns out that the homological algebrais just razzle dazzle, and can all be replaced by the single observation that if you write the equationsas the rows of a matrix then the number of solutions is the product of the elementary divisors in thesmith normal form of the matrix. we obtain the porc formulae for the number of r-generator groupsof p-class two for r  6. in addition, we obtain the porc formula for the number of p-class two groupsof order p^8.