## University of Sydney Algebra Seminar

# Youming Qiao (University of Technology Sydney)

## Friday 29 September, 12-1pm, Place: Carslaw 375

## 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.