$p$-group (reviewed)

A $p$-group is a group whose order is a power of a prime $p$. A result of Higman and Sims shows that the number of groups of order $p^k$ is $p^{(2/27 + o(1))k^3}$, and this can be combined with a result of Pyber to show that, asymptotically, 100% of groups are $p$-groups.