The relational complexity of linear groups acting on subspaces
Date
14/02/2024Metadata
Show full item recordAbstract
The relational complexity of a subgroup G of Sym(Ω) is a measure of the way in which the orbits of G on Ωk for various k determine the original action of G. Very few precise values of relational complexity are known. This paper determines the exact relational complexity of all groups lying between PSLn() and PGLn(), for an arbitrary field , acting on the set of 1-dimensional subspaces of n. We also bound the relational complexity of all groups lying between PSLn(q) and PΓLn(q), and generalise these results to the action on m-spaces for m at least 1.
Citation
Freedman , S D , Kelsey , V & Roney-Dougal , C 2024 , ' The relational complexity of linear groups acting on subspaces ' , Journal of Group Theory , vol. Ahead of Print . https://doi.org/10.1515/jgth-2023-0262
Publication
Journal of Group Theory
Status
Peer reviewed
ISSN
1433-5883Type
Journal article
Description
Funding: This work was supported by EPSRC grant no. EP/R014604/1, and also partially supported by a grant from the Simons Foundation. The first author was supported by the University of St Andrews (St Leonard’s International Doctoral Fees Scholarship & School of Mathematics and Statistics PhD Funding Scholarship), and by EPSRC grant no. EP/W522422/1. The second author is funded by the Heilbronn Institute.Collections
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