Primitive normalisers in quasipolynomial time
Abstract
The normaliser problem has as input two subgroups H and K of the symmetric group Sn, and asks for a generating set for NK(H): it is not known to have a subexponential time solution. It is proved in [Roney-Dougal & Siccha, 2020] that if H is primitive then the normaliser problem can be solved in quasipolynomial time. We show that for all subgroups H and K of Sn, in quasipolynomial time we can decide whether NSn(H) is primitive, and if so compute NK(H). Hence we reduce the question of whether one can solve the normaliser problem in quasipolynomial time to the case where the normaliser in Sn is known not to be primitive.
Citation
Chang , M S & Roney-Dougal , C M 2021 , ' Primitive normalisers in quasipolynomial time ' , Archiv der Mathematik , vol. First Online , ADMA-D-21-00337 . https://doi.org/10.1007/s00013-021-01670-5
Publication
Archiv der Mathematik
Status
Peer reviewed
ISSN
0003-889XType
Journal article
Description
Funding: The first author is supported by a Royal Society grant (RGF\EA\181005).Collections
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