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 $p^{2/27k^3+O(k^{5/2})}$ (Newman and Seeley), and lower bounded by $p^{2/27k^3-4/9k^2}$ (G. Higman, 1960). In this talk I will describe how to obtain an improved lower bound $p^{2/27k^3-O(k)}$. 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.