**Speaker:** Neil Saunders (Lausanne)

**Title:** *An Algorithm for Computing the Minimal
Permutation Degree of a Finite Nilpotent Group*

**Abstract:**

The minimal permutation degree of a finite group \(G\) is the smallest
non-negative integer \(n\) such that \(G\) embeds inside \(Sym(n)\). This
invariant is easy to define but very difficult to calculate.
Moreover, it doesn't behave well under algebraic constructions such as
(semi)direct product and homomorphic image. For example, it is possible for
the minimal degree of a homomorphic image to be strictly larger than that
of the group -- such groups are called *exceptional*.

In this talk, I will describe how this invariant may be calculated by a greedy algorithm for nilpotent groups and report on recent work with Britnell and Skyner on exceptional \(p\)-groups.