Journal of Algebraic Combinatorics

, Volume 33, Issue 1, pp 127–140

Non-abelian representations of the slim dense near hexagons on 81 and 243 points


DOI: 10.1007/s10801-010-0237-5

Cite this article as:
De Bruyn, B., Sahoo, B.K. & Sastry, N.S.N. J Algebr Comb (2011) 33: 127. doi:10.1007/s10801-010-0237-5


We prove that the near hexagon \(Q(5,2)\times\mathbb{L}_{3}\) has a non-abelian representation in the extra-special 2-group \(2^{1+12}_{+}\) and that the near hexagon Q(5,2)Q(5,2) has a non-abelian representation in the extra-special 2-group \(2^{1+18}_{-}\). The description of the non-abelian representation of Q(5,2)Q(5,2) makes use of a new combinatorial construction of this near hexagon.


Near hexagon Non-abelian representation Extra-special 2-group 

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsGhent UniversityGentBelgium
  2. 2.School of Mathematical SciencesNational Institute of Science Education and ResearchBhubaneswarIndia
  3. 3.Statistics and Mathematics UnitIndian Statistical InstituteBangaloreIndia