Computational Algebra Seminar: Saunders -- Exceptional Quotients of Permutation Groups

Neil Saunders (University of Bristol)

Thursday September 18, 3pm, Carslaw 535

"Exceptional Quotients of Permutation Groups"   

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 in general.
Moreover, it doesn’t behave well under algebraic constructions such as
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 maybe calculated by a 
greedy algorithm for nilpotent groups and report on recent work with
Britnell and Skyner on classifying exceptional groups of order p^5.