Limit to Infinity of Number of p-Groups of Order p^m

Theorem
Let $p$ be a prime number.

Let $m \in \N$ be a natural number

Let $\map \nu {p^n}$ denote the $\nu$ function of $p^n$: the number of group types of order $p^m$.

Then:
 * $\map \nu {p^m} = p^{A m^3}$

where:
 * $\ds \lim_{m \mathop \to \infty} A = \dfrac 2 {27}$