Bases for Primitive Permutation Groups and a Conjecture of Babai, Original Research Article

Abaseof a permutation groupGis a sequenceBof points from the permutation domain such that only the identity ofGfixesBpointwise. We show that primitive permutation groups with no alternating composition factors of degree greater thandand no classical composition factors of rank greater thandhave a base of size bounded above by a function ofd. This confirms a conjecture of Babai.