Bases for permutation groups and the Saxl graph

Let $G$ be a permutation group on a set $Omega$. A base for $G$, is a subset $B$ of $Omega$ such that the pointwise stabiliser of the elements of $B$ is trivial. There has been a large amount of recent research on the size of a base of a primitive permutation group, culminating with the recent proof of Pyber's Conjecture. At the same time there has been a large amount of work devoted to finding the primitive groups with a base of size two. For such groups we can define the Saxl graph of $G$ to be the graph with vertex set $Omega$ and two elements are joined by an edge if they are a base. I will discuss some recent work with Tim Burness that investigates some of the properties of this graph.

Join Zoom Meeting HERE!

Everyone is welcome and encouraged to attend.

For more info visit our Website and our YouTube Channel.