# Youming Qiao (University of Technology Sydney)

## Improved lower bound on the number of finite p-groups

The number of finite p-groups of order $$p^k$$ is known to be upper bounded by $$p^{2/27 k^3+O(k^{5/2})}$$ (Newman and Seeley), and lower bounded by $$p^{2/27 k^3-4/9 k^2}$$ (G. Higman, 1960). In this talk I will describe how to obtain an improved lower bound $$p^{2/27 k^3-O(k)}$$. Interestingly, the key idea is inspired by a result from random graph theory (Babai-Erdös-Selkow, 1980). This is based on a joint work with Yinan Li at UTS.