Polarized non-abelian representations of slim near-polar spaces
- Author
- Bart De Bruyn (UGent) and Binod Kumar Sahoo
- Organization
- 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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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8510636
- MLA
- De Bruyn, Bart, and Binod Kumar Sahoo. “Polarized Non-Abelian Representations of Slim near-Polar Spaces.” JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 44, no. 1, 2016, pp. 59–79, doi:10.1007/s10801-015-0653-7.
- 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. https://doi.org/10.1007/s10801-015-0653-7
- Chicago author-date
- 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. https://doi.org/10.1007/s10801-015-0653-7.
- Chicago author-date (all authors)
- 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. doi:10.1007/s10801-015-0653-7.
- 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.
- IEEE
- [1]B. De Bruyn and B. K. Sahoo, “Polarized non-abelian representations of slim near-polar spaces,” JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 44, no. 1, pp. 59–79, 2016.
@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}}, 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}}, language = {{eng}}, number = {{1}}, pages = {{59--79}}, title = {{Polarized non-abelian representations of slim near-polar spaces}}, url = {{http://doi.org/10.1007/s10801-015-0653-7}}, volume = {{44}}, year = {{2016}}, }
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