ALGB Seminar: Alice Devillers (The University of Western Australia)
Title: The distinguishing number of quasiprimitive and semiprimitive groups
Abstract: The distinguishing number of a permutation group G⩽Sym(Ω) is the smallest size of a partition of Ω such that only the identity of G fixes all the parts of the partition. In this paper, we determine the exact value of the distinguishing number of all finite semiprimitive and quasiprimitive permutation groups, extending earlier results of Cameron, Neumann, Saxl and Seress on finite primitive groups. In particular, we show that all imprimitive quasiprimitive groups have distinguishing number two, and all non-quasiprimitive semiprimitive groups have distinguishing number two, except for GL(2,3) acting on the eight non-zero vectors of (F_3)^2 which has distinguishing number three.