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Existence of non-abelian representations of the near hexagon Q(5,2)⊗Q(5,2)

Abstract

In [5], a new combinatorial model with four types of points and nine types of lines of the slim dense near hexagon Q(5,2)⊗Q(5,2) was provided and it was then used to construct a non-abelain representation of Q(5,2)⊗Q(5,2) in the extraspecial 2-group \(2_{-}^{1+18}\). In this paper, we give a direct proof for the existence of a non-abelian representation of Q(5,2)⊗Q(5,2) in \(2_{-}^{1+18}\).

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Acknowledgement

This research was supported by DST/SERB (Project No. SR/FTP/MS-001/2010), Government of India.

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Correspondence to BINOD KUMAR SAHOO.

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Communicating Editor: B V Rajarama Bhat

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SAHOO, B.K. Existence of non-abelian representations of the near hexagon Q(5,2)⊗Q(5,2) . Proc Math Sci 126, 143–151 (2016). https://doi.org/10.1007/s12044-016-0277-4

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  • DOI: https://doi.org/10.1007/s12044-016-0277-4

Keywords

  • Near hexagon
  • non-abelian representation
  • extraspecial 2-group.

2010 Mathematics Subject Classification.

  • 05B25.