## p-Group

A Finite Group of Order for a Prime is called a -group. Sylow proved that every Group of this form has a Power-commutator representation on generators defined by

 (1)

for , and
 (2)

for , . If is Prime and the number of Groups of order , then
 (3)

where
 (4)

(Higman 1960a,b).

Higman, G. Enumerating -Groups. I. Inequalities.'' Proc. London Math. Soc. 10, 24-30, 1960a.
Higman, G. Enumerating -Groups. II. Problems Whose Solution is PORC.'' Proc. London Math. Soc. 10, 566-582, 1960b.