On the uniqueness of the generalized octagon of order (2, 4)

Research output: Contribution to journalArticle


Colleges, School and Institutes

External organisations

  • School of Mathematics, Watson Building; University of Birmingham; Edgbaston Birmingham B15 2TT UK
  • Department of Mathematics and Computer Science, Technische Universiteit Eindhoven
  • Department of Mathematics, University of Auckland


The smallest known thick generalized octagon has order (2, 4) and can be constructed from the parabolic subgroups of the Ree group ^2F4(2). It is not known whether this generalized octagon is unique up to isomorphism. We show that it is unique up to isomorphism among those having a point a whose stabilizer in the automorphism group both fixes setwise every line on a and contains a subgroup that is regular on the set of 1024 points at maximal distance to a. Our proof uses extensively the classification of the groups of order dividing 29.


Original languageEnglish
Pages (from-to)369-393
Number of pages25
JournalJournal of Algebra
Publication statusPublished - 1 Jan 2015


  • Cayley graph, Generalized polygon, Groups of order a small power of 2, Incidence geometry, Octagon, Point-line geometry, Ree group