Computing normalisers of intransitive groups

The normaliser problem takes as input subgroups G and H of the symmetric group Sn, and asks one to compute NG(H). The fastest known algorithm for this problem is simply exponential, whilst more efficient algorithms are known for restricted classes of groups. In this paper, we will focus on groups wi...

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Bibliographic Details
Published inJournal of algebra Vol. 605; pp. 429 - 458
Main Authors Chang, Mun See, Jefferson, Christopher, Roney-Dougal, Colva M.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2022
Subjects
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Computational group theory
Permutation groups
Computational group theory
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Permutation groups
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Summary:The normaliser problem takes as input subgroups G and H of the symmetric group Sn, and asks one to compute NG(H). The fastest known algorithm for this problem is simply exponential, whilst more efficient algorithms are known for restricted classes of groups. In this paper, we will focus on groups with many orbits. We give a new algorithm for the normaliser problem for these groups that performs many orders of magnitude faster than previous implementations in GAP. We also prove that the normaliser problem for the special case G=Sn is at least as hard as computing the group of monomial automorphisms of a linear code over any field of fixed prime order.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2022.05.001