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

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Abstract
We prove that the near hexagon Q(5, 2) x L(3) has a non-abelian representation in the extra-special 2-group 21(+)(1+12) and that the near hexagon Q(5, 2) circle times 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) circle times Q(5, 2) makes use of a new combinatorial construction of this near hexagon.
Keywords
GENERALIZED QUADRANGLES, POLYGONS, Extra-special 2-group, Near hexagon, Non-abelian representation, SYMMETRY, SPACES, SPREAD, ORDER

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Citation

Please use this url to cite or link to this publication:

MLA
De Bruyn, Bart, et al. “Non-Abelian Representations of the Slim Dense near Hexagons on 81 and 243 Points.” JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 33, no. 1, 2011, pp. 127–40, doi:10.1007/s10801-010-0237-5.
APA
De Bruyn, B., Sahoo, B., & Sastry, N. (2011). Non-abelian representations of the slim dense near hexagons on 81 and 243 points. JOURNAL OF ALGEBRAIC COMBINATORICS, 33(1), 127–140. https://doi.org/10.1007/s10801-010-0237-5
Chicago author-date
De Bruyn, Bart, Binod Sahoo, and Narasimha Sastry. 2011. “Non-Abelian Representations of the Slim Dense near Hexagons on 81 and 243 Points.” JOURNAL OF ALGEBRAIC COMBINATORICS 33 (1): 127–40. https://doi.org/10.1007/s10801-010-0237-5.
Chicago author-date (all authors)
De Bruyn, Bart, Binod Sahoo, and Narasimha Sastry. 2011. “Non-Abelian Representations of the Slim Dense near Hexagons on 81 and 243 Points.” JOURNAL OF ALGEBRAIC COMBINATORICS 33 (1): 127–140. doi:10.1007/s10801-010-0237-5.
Vancouver
1.
De Bruyn B, Sahoo B, Sastry N. Non-abelian representations of the slim dense near hexagons on 81 and 243 points. JOURNAL OF ALGEBRAIC COMBINATORICS. 2011;33(1):127–40.
IEEE
[1]
B. De Bruyn, B. Sahoo, and N. Sastry, “Non-abelian representations of the slim dense near hexagons on 81 and 243 points,” JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 33, no. 1, pp. 127–140, 2011.
@article{2026929,
  abstract     = {{We prove that the near hexagon Q(5, 2) x L(3) has a non-abelian representation in the extra-special 2-group 21(+)(1+12) and that the near hexagon Q(5, 2) circle times 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) circle times Q(5, 2) makes use of a new combinatorial construction of this near hexagon.}},
  author       = {{De Bruyn, Bart and Sahoo, Binod and Sastry, Narasimha}},
  issn         = {{0925-9899}},
  journal      = {{JOURNAL OF ALGEBRAIC COMBINATORICS}},
  keywords     = {{GENERALIZED QUADRANGLES,POLYGONS,Extra-special 2-group,Near hexagon,Non-abelian representation,SYMMETRY,SPACES,SPREAD,ORDER}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{127--140}},
  title        = {{Non-abelian representations of the slim dense near hexagons on 81 and 243 points}},
  url          = {{http://doi.org/10.1007/s10801-010-0237-5}},
  volume       = {{33}},
  year         = {{2011}},
}

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