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

2010/03/24 by Bart De Bruyn, De Bruyn, B., Binod Kumar Sahoo +7
Computer Science · Engineering · Mathematics · #05B25 #Algebraic structures and combinatorial models #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:05B25

paper · pdf · doi:10.48550/arxiv.1003.4645

arxiv created 2010/03/24 · openalex publication_date 2010/03/24 · arxiv updated 2010/03/25 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We prove that the near hexagon Q(5,2) × \mathbbL₃ has a non-abelian representation in the extra-special 2-group 2¹⁺¹²₊ and that the near hexagon Q(5,2) ⊗ Q(5,2) has a non-abelian representation in the extra-special 2-group 2¹⁺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.

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