Primitive flag-transitive generalized hexagons and octagons

2007/04/21 by Csaba Schneider, Hendrik Van Maldeghem, Schneider, Csaba +1
Mathematics · #05B25 #20B15 #20B25 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.CO #math.GR #msc:05B25 #msc:20B15 #msc:20B25

paper · pdf · doi:10.48550/arxiv.0704.2845

forgot to upload the appendices in version 1, and this is rectified in version 2. erased cross-ref keys in version 3. Minor revision in version 4 to implement the suggestion by the referee (new section at the end, extended acknowledgment, simpler proof for Lemma 4.2)

openalex publication_date 2007/04/21 · arxiv created 2008/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that an automorphism group G acts flag-transitively on a finite generalized hexagon or octagon \cS, and suppose that the action on both the point and line set is primitive. We show that G is an almost simple group of Lie type, that is, the socle of G is a simple Chevalley group.

Related

• Point-primitive generalised hexagons and octagons
• Point-primitive generalised hexagons and octagons and projective linear groups
• Generalised polygons admitting a point-primitive almost simple group of Suzuki or Ree type
• Flag-transitive point-primitive quasi-symmetric 2-designs and exceptional groups of Lie type
• Almost simple groups of Lie type and symmetric designs with λ prime