Conjecture that most finite groups are nilpotent

This article is about a conjecture. View all conjectures and open problems

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 $n$. The conjecture is that:

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

Related facts

• Higman-Sims asymptotic formula on number of groups of prime power order
• Pyber's theorem on logarithmic quotient of number of nilpotent groups to number of groups approaching unity