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Polarized non-abelian representations of slim near-polar spaces

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Abstract
In (Bull Belg Math Soc Simon Stevin 4:299-316, 1997), Shult introduced a class of parapolar spaces, the so-called near-polar spaces. We introduce here the notion of a polarized non-abelian representation of a slim near-polar space, that is, a near-polar space in which every line is incident with precisely three points. For such a polarized non-abelian representation, we study the structure of the corresponding representation group, enabling us to generalize several of the results obtained in Sahoo and Sastry (J Algebraic Comb 29:195-213, 2009) for non-abelian representations of slim dense near hexagons. We show that with every polarized non-abelian representation of a slim near-polar space, there is an associated polarized projective embedding.
Keywords
Near-polar space, Universal/Polarized non-abelian representation, Universal projective embedding, Minimal polarized embedding, Extraspecial 2-group, Combinatorial group theory, DENSE, GEOMETRIES, EMBEDDINGS, ORDER

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

Chicago
De Bruyn, Bart, and Binod Kumar Sahoo. 2016. “Polarized Non-abelian Representations of Slim Near-polar Spaces.” Journal of Algebraic Combinatorics 44 (1): 59–79.
APA
De Bruyn, B., & Sahoo, B. K. (2016). Polarized non-abelian representations of slim near-polar spaces. JOURNAL OF ALGEBRAIC COMBINATORICS, 44(1), 59–79.
Vancouver
1.
De Bruyn B, Sahoo BK. Polarized non-abelian representations of slim near-polar spaces. JOURNAL OF ALGEBRAIC COMBINATORICS. 2016;44(1):59–79.
MLA
De Bruyn, Bart, and Binod Kumar Sahoo. “Polarized Non-abelian Representations of Slim Near-polar Spaces.” JOURNAL OF ALGEBRAIC COMBINATORICS 44.1 (2016): 59–79. Print.
@article{8510636,
  abstract     = {In (Bull Belg Math Soc Simon Stevin 4:299-316, 1997), Shult introduced a class of parapolar spaces, the so-called near-polar spaces. We introduce here the notion of a polarized non-abelian representation of a slim near-polar space, that is, a near-polar space in which every line is incident with precisely three points. For such a polarized non-abelian representation, we study the structure of the corresponding representation group, enabling us to generalize several of the results obtained in Sahoo and Sastry (J Algebraic Comb 29:195-213, 2009) for non-abelian representations of slim dense near hexagons. We show that with every polarized non-abelian representation of a slim near-polar space, there is an associated polarized projective embedding.},
  author       = {De Bruyn, Bart and Sahoo, Binod Kumar},
  issn         = {0925-9899},
  journal      = {JOURNAL OF ALGEBRAIC COMBINATORICS},
  keyword      = {Near-polar space,Universal/Polarized non-abelian representation,Universal projective embedding,Minimal polarized embedding,Extraspecial 2-group,Combinatorial group theory,DENSE,GEOMETRIES,EMBEDDINGS,ORDER},
  language     = {eng},
  number       = {1},
  pages        = {59--79},
  title        = {Polarized non-abelian representations of slim near-polar spaces},
  url          = {http://dx.doi.org/10.1007/s10801-015-0653-7},
  volume       = {44},
  year         = {2016},
}

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