Abstract
We investigate the normaliser problem, that is, given 𝐺, 𝐻 ≤ 𝑆โ, compute 𝑁[sub]𝐺(𝐻). The fastest known theoretical algorithm for this problem is simply exponential, but more e๏ฌcient 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](𝑆โ)(𝐻) for highly intransitive groups 𝐻 ≤ 𝑆โ and for some subclasses that perform substantially faster than previous implementations in the computer algebra system GAP.
Type
Thesis, PhD Doctor of Philosophy
Rights
Creative Commons Attribution-ShareAlike 4.0 International
https://creativecommons.org/licenses/by-sa/4.0/