The relational complexity of linear groups acting on subspaces

Saul D. Freedman, Veronica Kelsey, Colva M. Roney-Dougal

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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 (F) and PGLn (F), for an arbitrary field F, acting on the set of 1-dimensional subspaces of Fn. 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 ≥ 1.

Original languageEnglish
Number of pages29
JournalJournal of Group Theory
DOIs
Publication statusAccepted/In press - 2024

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