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Characterizations of the Suzuki tower near polygons

Anurag Bishnoi (UGent) and Bart De Bruyn (UGent)
(2017) DESIGNS CODES AND CRYPTOGRAPHY. 84(1-2). p.115-133
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Abstract
In recent work, we constructed a new near octagon G from certain involutions of the finite simple group G(2)(4) and showed a correspondence between the Suzuki tower of finite simple groups, L-3(2) < U-3(3) < J(2) < G(2)(4) < Suz, and the tower of near polygons, H(2, 1) subset of H(2)(D) subset of HJ subset of G. Here we characterize each of these near polygons (except for the first one) as the unique near polygon of the given order and diameter containing an isometrically embedded copy of the previous near polygon of the tower. In particular, our characterization of the Hall-Janko near octagon HJ is similar to an earlier characterization due to Cohen and Tits who proved that it is the unique regular near octagon with parameters (2, 4; 0, 3), but instead of regularity we assume existence of an isometrically embedded dual split Cayley hexagon, H(2)(D). We also give a complete classification of near hexagons of order (2, 2) and use it to prove the uniqueness result for H(2)(D).
Keywords
SPORADIC SIMPLE-GROUP, INVOLUTION GEOMETRY, GRAPHS, Near polygon, Generalized polygon, Suzuki tower

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MLA
Bishnoi, Anurag, and Bart De Bruyn. “Characterizations of the Suzuki Tower near Polygons.” DESIGNS CODES AND CRYPTOGRAPHY, vol. 84, no. 1–2, 2017, pp. 115–33, doi:10.1007/s10623-016-0230-7.
APA
Bishnoi, A., & De Bruyn, B. (2017). Characterizations of the Suzuki tower near polygons. DESIGNS CODES AND CRYPTOGRAPHY, 84(1–2), 115–133. https://doi.org/10.1007/s10623-016-0230-7
Chicago author-date
Bishnoi, Anurag, and Bart De Bruyn. 2017. “Characterizations of the Suzuki Tower near Polygons.” DESIGNS CODES AND CRYPTOGRAPHY 84 (1–2): 115–33. https://doi.org/10.1007/s10623-016-0230-7.
Chicago author-date (all authors)
Bishnoi, Anurag, and Bart De Bruyn. 2017. “Characterizations of the Suzuki Tower near Polygons.” DESIGNS CODES AND CRYPTOGRAPHY 84 (1–2): 115–133. doi:10.1007/s10623-016-0230-7.
Vancouver
1.
Bishnoi A, De Bruyn B. Characterizations of the Suzuki tower near polygons. DESIGNS CODES AND CRYPTOGRAPHY. 2017;84(1–2):115–33.
IEEE
[1]
A. Bishnoi and B. De Bruyn, “Characterizations of the Suzuki tower near polygons,” DESIGNS CODES AND CRYPTOGRAPHY, vol. 84, no. 1–2, pp. 115–133, 2017.
@article{8548622,
  abstract     = {{In recent work, we constructed a new near octagon G from certain involutions of the finite simple group G(2)(4) and showed a correspondence between the Suzuki tower of finite simple groups, L-3(2) < U-3(3) < J(2) < G(2)(4) < Suz, and the tower of near polygons, H(2, 1) subset of H(2)(D) subset of HJ subset of G. Here we characterize each of these near polygons (except for the first one) as the unique near polygon of the given order and diameter containing an isometrically embedded copy of the previous near polygon of the tower. In particular, our characterization of the Hall-Janko near octagon HJ is similar to an earlier characterization due to Cohen and Tits who proved that it is the unique regular near octagon with parameters (2, 4; 0, 3), but instead of regularity we assume existence of an isometrically embedded dual split Cayley hexagon, H(2)(D). We also give a complete classification of near hexagons of order (2, 2) and use it to prove the uniqueness result for H(2)(D).}},
  author       = {{Bishnoi, Anurag and De Bruyn, Bart}},
  issn         = {{0925-1022}},
  journal      = {{DESIGNS CODES AND CRYPTOGRAPHY}},
  keywords     = {{SPORADIC SIMPLE-GROUP,INVOLUTION GEOMETRY,GRAPHS,Near polygon,Generalized polygon,Suzuki tower}},
  language     = {{eng}},
  number       = {{1-2}},
  pages        = {{115--133}},
  title        = {{Characterizations of the Suzuki tower near polygons}},
  url          = {{http://dx.doi.org/10.1007/s10623-016-0230-7}},
  volume       = {{84}},
  year         = {{2017}},
}

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