Point-primitive generalised hexagons and octagons

2014/10/09 by John Bamberg, S. P. Glasby, Bamberg, John +7
Mathematics · #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1410.3423

openalex publication_date 2014/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2008, Schneider and Van Maldeghem proved that if a group acts flag-transitively, point-primitively, and line-primitively on a generalised hexagon or generalised octagon, then it is an almost simple group of Lie type. We show that point-primitivity is sufficient for the same conclusion, regardless of the action on lines or flags. This result narrows the search for generalised hexagons or octagons with point- or line-primitive collineation groups beyond the classical examples, namely the two generalised hexagons and one generalised octagon admitting the Lie type groups G₂(q), ³D₄(q), and ²F₄(q), respectively.

Citations

• On the orbit-sizes of permutation groups containing elements separating finite subsets

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