[GAP Forum] Groups of order p^n and exponent p

[Mike Newman]

Hi Alan,

You are right about Higman's lower bound.

A simple modification of Higman's argument gives that there are  at least
p^{2*n*n*(n-9)/27} groups with order p^n, class 2 and exponent p.
So asymptotically there are also p^{2(n^3)/27} groups with order p^n,
class 2 and exponent p.

All the best,

      Mike (Newman)