Gabriel Verret

A permutation group G on X is transitive if for every x and y in X, there exists g in G mapping x to y. The group G is called primitive if, in addition, it preserves no nontrivial partition of X. Let Gamma be a vertex-primitive digraph, that is, its...

One version of the Polycirculant Conjecture is that every finite vertex-transitive digraph admits a non-trivial semiregular automorphism. I will give an overview of the status of this conjecture, as well as describe some recent progress with Michael...