Pyber's theorem on logarithmic quotient of number of nilpotent groups to number of groups approaching unity

Statement
For any natural number $$n$$, define $$g(n)$$ as the number of fact about::finite groups whose order is at most $$n$$, and let $$g_{nil}(n)$$ be the number of fact about::finite nilpotent groups whose order is at most $$n$$. Then:

$$\! \lim_{n \to \infty} \frac{\log (g_{nil}(n))}{\log (g(n))} = 1$$

Related facts

 * Higman-Sims asymptotic formula for number of groups of prime power order
 * Conjecture that most finite groups are nilpotent