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Computing normalisers of highly intransitive groups

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dc.contributor.advisorJefferson, Christopher Anthony
dc.contributor.advisorRoney-Dougal, Colva Mary
dc.contributor.authorChang, Mun See
dc.coverage.spatialx, 146 p.en_US
dc.date.accessioned2021-06-24T12:12:15Z
dc.date.available2021-06-24T12:12:15Z
dc.date.issued2021-06-30
dc.identifier.urihttps://hdl.handle.net/10023/23416
dc.description.abstractWe 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.en_US
dc.description.sponsorship"This work was supported by the University of St Andrews (School of Computer Science and St Leonard’s College Scholarship)." -- Fundingen
dc.language.isoenen_US
dc.publisherUniversity of St Andrews
dc.relationComputing normalisers of highly intransitive groups (thesis data) Chang, M.S., University of St Andrews, 21 April 2021. DOI: https://doi.org/10.17630/710dfd8d-356b-4080-b2ad-c6791b7c21feen
dc.relation.urihttps://doi.org/10.17630/710dfd8d-356b-4080-b2ad-c6791b7c21fe
dc.rightsCreative Commons Attribution-ShareAlike 4.0 International*
dc.rights.urihttps://creativecommons.org/licenses/by-sa/4.0/*
dc.subjectPermutation groupsen_US
dc.subjectComputational group theoryen_US
dc.subjectGAPen_US
dc.subject.lccQA175.C5
dc.subject.lcshPermutation groupsen
dc.subject.lcshGroup theory--Data processingen
dc.titleComputing normalisers of highly intransitive groupsen_US
dc.typeThesisen_US
dc.contributor.sponsorUniversity of St Andrews. School of Computer Scienceen_US
dc.contributor.sponsorUniversity of St Andrews. St Leonard's Collegeen_US
dc.type.qualificationlevelDoctoralen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US
dc.publisher.departmentCentre for Interdisciplinary Research in Computational Algebra (CIRCA)en_US
dc.identifier.doihttps://doi.org/10.17630/sta/77


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