THE RELATIONAL COMPLEXITY OF LINEAR GROUPS ACTING ON SUBSPACES

SAUL D. FREEDMAN; Veronica Kelsey; COLVA M.   RONEY-DOUGAL

THE RELATIONAL COMPLEXITY OF LINEAR GROUPS ACTING ON SUBSPACES

SAUL D. FREEDMAN, Veronica Kelsey, COLVA M. RONEY-DOUGAL

Pure Mathematics

Research output: Contribution to journal › Article › peer-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 Ω^k 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 PSL_n(F) and PGL_n(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 PSL_n(q) and PΓL_n(q), and generalise these results to the action on m-spaces for m ≥ 1.

Original language	English
Journal	Journal of Group Theory
Publication status	Accepted/In press - 8 Dec 2023

Keywords

Relational complexity
linear groups
subspace actions

Cite this

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abstract = "The relational complexity of a subgroup G of Sym(Ω) is a measure of the way inwhich 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.",

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AU - RONEY-DOUGAL, COLVA M.

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N2 - The relational complexity of a subgroup G of Sym(Ω) is a measure of the way inwhich 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.

AB - The relational complexity of a subgroup G of Sym(Ω) is a measure of the way inwhich 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.

KW - Relational complexity

KW - linear groups

KW - subspace actions

M3 - Article

SN - 1433-5883

JO - Journal of Group Theory

JF - Journal of Group Theory

ER -

THE RELATIONAL COMPLEXITY OF LINEAR GROUPS ACTING ON SUBSPACES

Abstract

Keywords

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