Vertex-primitive s-arc-transitive digraphs of almost simple groups

Lei Chen

doi:10.26182/ex3t-c666

Vertex-primitive s-arc-transitive digraphs of almost simple groups

Lei Chen

School of Physics, Mathematics and Computing

Research output: Thesis › Doctoral Thesis

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Abstract

This thesis is to investigate the s-arc-transitivity of the vertex-primitive digraphs for almost simple groups. The problem was first proposed by Praeger and has been conjectured that s is bounded above by 2. We study different types of almost simple groups in this context, including symplectic groups, the small ree groups, Suzuki groups and other exceptional groups of Lie type. It turns out that all of those groups are at most 2-arc-transitive. We also construct infinite families of G-vertex primitive G-arc-transitive digraphs for almost simple groups admitting the small ree and Suzuki groups in this thesis.

Original language	English
Qualification	Doctor of Philosophy
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Giudici, Michael, Supervisor Praeger, Cheryl, Supervisor
Award date	13 Mar 2024
DOIs	https://doi.org/10.26182/ex3t-c666
Publication status	Unpublished - 2023

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10.26182/ex3t-c666

THESIS - DOCTOR OF PHILOSOPHY - CHEN Lei - 2023
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1 Abstract/Meeting Abstract
1 Article

VERTEX-PRIMITIVE s-ARC-TRANSITIVE DIGRAPHS OF ALMOST SIMPLE GROUPS
Chen, L., 16 Oct 2024, (E-pub ahead of print) In: Bulletin of the Australian Mathematical Society. 110, 3, p. 566-567 2 p.
Research output: Contribution to journal › Abstract/Meeting Abstract › peer-review
Vertex-primitive s-arc-transitive digraphs admitting a Suzuki or Ree group
Chen, L., Giudici, M. & Praeger, C. E., Aug 2023, In: European Journal of Combinatorics. 112, 103729.
Research output: Contribution to journal › Article › peer-review
2 Citations (Web of Science)

Cite this

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title = "Vertex-primitive s-arc-transitive digraphs of almost simple groups",

abstract = "This thesis is to investigate the s-arc-transitivity of the vertex-primitive digraphs for almost simple groups. The problem was first proposed by Praeger and has been conjectured that s is bounded above by 2. We study different types of almost simple groups in this context, including symplectic groups, the small ree groups, Suzuki groups and other exceptional groups of Lie type. It turns out that all of those groups are at most 2-arc-transitive. We also construct infinite families of G-vertex primitive G-arc-transitive digraphs for almost simple groups admitting the small ree and Suzuki groups in this thesis.",

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AB - This thesis is to investigate the s-arc-transitivity of the vertex-primitive digraphs for almost simple groups. The problem was first proposed by Praeger and has been conjectured that s is bounded above by 2. We study different types of almost simple groups in this context, including symplectic groups, the small ree groups, Suzuki groups and other exceptional groups of Lie type. It turns out that all of those groups are at most 2-arc-transitive. We also construct infinite families of G-vertex primitive G-arc-transitive digraphs for almost simple groups admitting the small ree and Suzuki groups in this thesis.

KW - digraph

KW - almost simple group

KW - primitive group

KW - s-arc-transitive

U2 - 10.26182/ex3t-c666

DO - 10.26182/ex3t-c666

M3 - Doctoral Thesis

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Vertex-primitive s-arc-transitive digraphs of almost simple groups

Abstract

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Research output

VERTEX-PRIMITIVE s-ARC-TRANSITIVE DIGRAPHS OF ALMOST SIMPLE GROUPS

Vertex-primitive s-arc-transitive digraphs admitting a Suzuki or Ree group

Cite this