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 Finite group (?)s whose order is at most $n$, and let $g_{nil}(n)$ be the number of Finite nilpotent group (?)s 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