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Description

The distinguishing number of a permutation group $G \leq \Sym(X)$ is the smallest number of colours required to colour the points of $X$ such that only the identity of $G$ preserves the colouring. The distinguishing number of a graph, in the traditional sense, is simply the distinguishing number of its automorphism group. Seress proved that every primitive group of degree $n$ other than $\Alt(n)$ and $\Sym(n)$ has distinguishing number 2, except for a short list of known examples (with distinguishing number 3 or 4). In this talk, I will overview previous work on the distinguishing number of groups, before discussing recent joint work with Alice Devillers and Luke Morgan on the distinguishing number of semiprimitive groups. I will highlight the application of our result to graphs.