On the number of $p$-elements in finite groups

Abstract: Given a finite group $G$ and a prime $p$ dividing its order, we consider the ratio between the number of $p$-elements and the order of a Sylow $p$-subgroup of $G$. Frobenius proved that this ratio is always an integer, but no combinatorial interpretation of this number seems to be known.

We will talk about the search for a lower bound on this ratio in terms of the number of Sylow $p$-subgroups of $G$.

group theory

Audience: researchers in the topic

Finite Groups in Valencia

Series comments: The seminar meets weekly from February 26th to March 30th 2021.

For a detailed schedule and registration details, please visit the seminar webpage at

sites.google.com/view/finite-groups-seminar2021