Journal of Algebraic Combinatorics

, Volume 44, Issue 1, pp 59–79

Polarized non-abelian representations of slim near-polar spaces


DOI: 10.1007/s10801-015-0653-7

Cite this article as:
De Bruyn, B. & Sahoo, B.K. J Algebr Comb (2016) 44: 59. doi:10.1007/s10801-015-0653-7


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.


Near-polar space Universal/ Polarized non-abelian representation Universal projective embedding Minimal polarized embedding Extraspecial 2-group  Combinatorial group theory 

Mathematics Subject Classification

05B25 51A45 51A50 20F05 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsGhent UniversityGentBelgium
  2. 2.School of Mathematical SciencesNational Institute of Science Education and ResearchOdishaIndia