Point-primitive generalised hexagons and octagons

John Bamberg, Stephen Glasby, Tomasz Popiel, Cheryl Praeger, Csaba Schneider

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The only known examples of finite generalised hexagons and octagons arise from the finite almost simple groups of Lie type G2, D43, and F42. These groups act transitively on flags, primitively on points, and primitively on lines. The best converse result prior to the writing of this paper was that of Schneider and Van Maldeghem (2008): if a group G acts flag-transitively, point-primitively, and line-primitively on a finite generalised hexagon or octagon, then G is an almost simple group of Lie type. We strengthen this result by showing that the same conclusion holds under the sole assumption of point-primitivity.
Original languageEnglish
Pages (from-to)186-204
Number of pages19
JournalJournal of Combinatorial Theory, Series A
Volume147
DOIs
Publication statusPublished - Apr 2017

Fingerprint

Generalized Hexagon
Groups of Lie Type
Simple group
Octagon
Line
Converse

Cite this

Bamberg, J., Glasby, S., Popiel, T., Praeger, C., & Schneider, C. (2017). Point-primitive generalised hexagons and octagons. Journal of Combinatorial Theory, Series A, 147, 186-204. https://doi.org/10.1016/j.jcta.2016.11.008
Bamberg, John ; Glasby, Stephen ; Popiel, Tomasz ; Praeger, Cheryl ; Schneider, Csaba. / Point-primitive generalised hexagons and octagons. In: Journal of Combinatorial Theory, Series A. 2017 ; Vol. 147. pp. 186-204.
@article{76b7dbedc43646288db2439faf38a223,
title = "Point-primitive generalised hexagons and octagons",
abstract = "The only known examples of finite generalised hexagons and octagons arise from the finite almost simple groups of Lie type G2, D43, and F42. These groups act transitively on flags, primitively on points, and primitively on lines. The best converse result prior to the writing of this paper was that of Schneider and Van Maldeghem (2008): if a group G acts flag-transitively, point-primitively, and line-primitively on a finite generalised hexagon or octagon, then G is an almost simple group of Lie type. We strengthen this result by showing that the same conclusion holds under the sole assumption of point-primitivity.",
keywords = "Generalised hexagon, Generalised octagon, Generalised polygon, Primitive permutation group",
author = "John Bamberg and Stephen Glasby and Tomasz Popiel and Cheryl Praeger and Csaba Schneider",
year = "2017",
month = "4",
doi = "10.1016/j.jcta.2016.11.008",
language = "English",
volume = "147",
pages = "186--204",
journal = "Journal of Combinatorial Theory - Series A",
issn = "0021-9800",
publisher = "Academic Press Inc.",

}

Bamberg, J, Glasby, S, Popiel, T, Praeger, C & Schneider, C 2017, 'Point-primitive generalised hexagons and octagons', Journal of Combinatorial Theory, Series A, vol. 147, pp. 186-204. https://doi.org/10.1016/j.jcta.2016.11.008

Point-primitive generalised hexagons and octagons. / Bamberg, John; Glasby, Stephen; Popiel, Tomasz; Praeger, Cheryl; Schneider, Csaba.

In: Journal of Combinatorial Theory, Series A, Vol. 147, 04.2017, p. 186-204.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Point-primitive generalised hexagons and octagons

AU - Bamberg, John

AU - Glasby, Stephen

AU - Popiel, Tomasz

AU - Praeger, Cheryl

AU - Schneider, Csaba

PY - 2017/4

Y1 - 2017/4

N2 - The only known examples of finite generalised hexagons and octagons arise from the finite almost simple groups of Lie type G2, D43, and F42. These groups act transitively on flags, primitively on points, and primitively on lines. The best converse result prior to the writing of this paper was that of Schneider and Van Maldeghem (2008): if a group G acts flag-transitively, point-primitively, and line-primitively on a finite generalised hexagon or octagon, then G is an almost simple group of Lie type. We strengthen this result by showing that the same conclusion holds under the sole assumption of point-primitivity.

AB - The only known examples of finite generalised hexagons and octagons arise from the finite almost simple groups of Lie type G2, D43, and F42. These groups act transitively on flags, primitively on points, and primitively on lines. The best converse result prior to the writing of this paper was that of Schneider and Van Maldeghem (2008): if a group G acts flag-transitively, point-primitively, and line-primitively on a finite generalised hexagon or octagon, then G is an almost simple group of Lie type. We strengthen this result by showing that the same conclusion holds under the sole assumption of point-primitivity.

KW - Generalised hexagon

KW - Generalised octagon

KW - Generalised polygon

KW - Primitive permutation group

UR - http://www.scopus.com/inward/record.url?scp=85003876189&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/pointprimitive-generalised-hexagons-octagons

U2 - 10.1016/j.jcta.2016.11.008

DO - 10.1016/j.jcta.2016.11.008

M3 - Article

VL - 147

SP - 186

EP - 204

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0021-9800

ER -