Subgroups of classical groups that are transitive on subspaces

Michael Giudici; S. P. Glasby; Cheryl E. Praeger

doi:10.1016/j.jalgebra.2023.08.032

Subgroups of classical groups that are transitive on subspaces

Michael Giudici, S. P. Glasby, Cheryl E. Praeger

Research output: Contribution to journal › Article › peer-review

2 Citations (Web of Science)

Abstract

For each finite classical group G, we classify the subgroups of G which act transitively on a G-invariant set of subspaces of the natural module, where the subspaces are either totally isotropic or nondegenerate. Our proof uses the classification of the maximal factorisations of almost simple groups. As a first application of these results we classify all point-transitive subgroups of automorphisms of finite thick classical generalised quadrangles.

Original language	English
Pages (from-to)	804-868
Number of pages	65
Journal	Journal of Algebra
Volume	636
DOIs	https://doi.org/10.1016/j.jalgebra.2023.08.032
Publication status	Published - 15 Dec 2023

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10.1016/j.jalgebra.2023.08.032Licence: CC BY

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title = "Subgroups of classical groups that are transitive on subspaces",

abstract = "For each finite classical group G, we classify the subgroups of G which act transitively on a G-invariant set of subspaces of the natural module, where the subspaces are either totally isotropic or nondegenerate. Our proof uses the classification of the maximal factorisations of almost simple groups. As a first application of these results we classify all point-transitive subgroups of automorphisms of finite thick classical generalised quadrangles.",

keywords = "Classical groups, Non-degenerate, Totally isotropic, Totally singular, Transitive actions",

author = "Michael Giudici and Glasby, {S. P.} and Praeger, {Cheryl E.}",

note = "Funding Information: The authors gratefully acknowledge the support of the Australian Research Council (ARC) Discovery Project Grants DP160102323 and DP190100450 . We thank the referee for carefully reading our manuscript and for numerous helpful suggestions. Publisher Copyright: {\textcopyright} 2023 The Authors",

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AU - Giudici, Michael

AU - Glasby, S. P.

AU - Praeger, Cheryl E.

N1 - Funding Information: The authors gratefully acknowledge the support of the Australian Research Council (ARC) Discovery Project Grants DP160102323 and DP190100450 . We thank the referee for carefully reading our manuscript and for numerous helpful suggestions. Publisher Copyright: © 2023 The Authors

PY - 2023/12/15

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N2 - For each finite classical group G, we classify the subgroups of G which act transitively on a G-invariant set of subspaces of the natural module, where the subspaces are either totally isotropic or nondegenerate. Our proof uses the classification of the maximal factorisations of almost simple groups. As a first application of these results we classify all point-transitive subgroups of automorphisms of finite thick classical generalised quadrangles.

AB - For each finite classical group G, we classify the subgroups of G which act transitively on a G-invariant set of subspaces of the natural module, where the subspaces are either totally isotropic or nondegenerate. Our proof uses the classification of the maximal factorisations of almost simple groups. As a first application of these results we classify all point-transitive subgroups of automorphisms of finite thick classical generalised quadrangles.

KW - Classical groups

KW - Non-degenerate

KW - Totally isotropic

KW - Totally singular

KW - Transitive actions

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VL - 636

SP - 804

EP - 868

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Subgroups of classical groups that are transitive on subspaces

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Complexity of group algorithms and statistical fingerprints of groups

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Subgroups of classical groups that are transitive on subspaces

Abstract

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Complexity of group algorithms and statistical fingerprints of groups

Permutation groups: factorisations, structure and applications

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