# Grad students algebra seminar: Tzoor Plotnikov (HUJI)

Date:
Sun, 23/05/202110:00-11:30
Location:
Room 110, Manchester Building, Jerusalem, Israel
Title: 5 things you didn't know about the commuting probabilities of finite groups

Abstract: The commuting probability $P(G)$, of a finite group $G$ is defined to be the probability of a random pair of elements to commute.

It is a classical result that given a finite group, if more than five eights of pairs of elements commute, then the group is abelian.

We will go over a result of Sean Eberhard from 2015 that shows that this phenomenon can be extended even further, in the sense that if $p$ is the commuting probability of any group, then there is some $\varepsilon>0$ such that no finite group has commuting probability between $p$ and $p+\varepsilon$.