Computing normalisers of highly intransitive groups

Student thesis: Doctoral Thesis (PhD)


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 Award30 Jun 2021
Original languageEnglish
Awarding Institution
  • University of St Andrews
SupervisorChristopher Anthony Jefferson (Supervisor) & Colva Roney-Dougal (Supervisor)


  • Permutation groups
  • Computational group theory
  • GAP

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