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

From Groupprops
Jump to: navigation, search

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