Record number :

682246

Title of article :

ON GRAHAM HIGMANʹʹS FAMOUS PORC PAPER

Author/Authors :

وان لي، مايكل نويسنده Vaughan-Lee, Michael

Issue Information :

فصلنامه با شماره پیاپی 0 سال 2012

Pages :

15

From page :

65

To page :

79

Abstract :

Abstract. We investigate Graham Higmanʹs paper Enumerating p-groups, II, in which he formulated
his famous PORC conjecture. We are able to simplify some of the theory. In particular, Higmanʹs
paper contains FIve pages of homological algebra which he uses in his proof that the number of solutions
in a FInite FIeld to a FInite set of monomial equations is PORC. It turns out that the homological algebra
is just razzle dazzle, and can all be replaced by the single observation that if you write the equations
as the rows of a matrix then the number of solutions is the product of the elementary divisors in the
Smith normal form of the matrix. We obtain the PORC formulae for the number of r-generator groups
of p-class two for r 6. In addition, we obtain the PORC formula for the number of p-class two groups
of order p^8.

Journal title :

International Journal of Group Theory

Journal title :

International Journal of Group Theory

Serial Year :

2012

Link To Document :