Computing normalisers of intransitive groups
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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.
Chang , M S , Jefferson , C A & Roney-Dougal , C M 2022 , ' Computing normalisers of intransitive groups ' , Journal of Algebra , vol. 605 , pp. 429-458 . https://doi.org/10.1016/j.jalgebra.2022.05.001
Journal of Algebra
DescriptionFunding: The first and third authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Groups, Representations and Applications: New perspectives”, where work on this paper was undertaken. This work was supported by EPSRC grant no EP/R014604/1. This work was also partially supported by a grant from the Simons Foundation. The first and second authors are supported by the Royal Society (RGF\EA\181005 and URF\R\180015).
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