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

  • Authors:
  • B. Bruyn;B. K. Sahoo;N. S. Sastry

  • Affiliations:
  • Department of Mathematics, Ghent University, Gent, Belgium 9000;School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, India 751005;Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore, India 560059

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2011

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Abstract

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)驴 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)驴 Q(5,2) makes use of a new combinatorial construction of this near hexagon.