Computing normalisers of highly intransitive groups

Abstract

We investigate the normaliser problem, that is, given 𝐺; 𝐻 ≤ 𝑆ₙ, compute 𝑁[sub]𝐺(𝐻).
The fastest known theoretical algorithm for this problem is simply exponential, but
more efficient algorithms are known for some restriction of classes for 𝐺 and 𝐻. In this
thesis, we will focus on highly intransitive groups, which are groups with many orbits.
We give new algorithms to compute 𝑁[sub](𝑆ₙ)
(𝐻) for highly intransitive groups 𝐻 ≤ 𝑆ₙ and
for some subclasses that perform substantially faster than previous implementations in
the computer algebra system GAP.

Date of Award	30 Jun 2021
Original language	English
Awarding Institution	University of St Andrews
Supervisor	Christopher Anthony Jefferson (Supervisor) & Colva Roney-Dougal (Supervisor)