Journal of Algebraic Combinatorics

, Volume 29, Issue 2, pp 195–213 | Cite as

On the order of a non-abelian representation group of a slim dense near hexagon

Article

Abstract

In this paper we study the possible orders of a non-abelian representation group of a slim dense near hexagon. We prove that if the representation group R of a slim dense near hexagon S is non-abelian, then R is a 2-group of exponent 4 and |R|=2β, 1+NPdim(S)≤β≤1+dimV(S), where NPdim(S) is the near polygon embedding dimension of S and dimV(S) is the dimension of the universal representation module V(S) of S. Further, if β=1+NPdim(S), then R is necessarily an extraspecial 2-group. In that case, we determine the type of the extraspecial 2-group in each case. We also deduce that the universal representation group of S is a central product of an extraspecial 2-group and an abelian 2-group of exponent at most 4.

Keywords

Near polygons Non-abelian representations Generalized quadrangles Extraspecial 2-groups 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of TechnologyRourkelaIndia
  2. 2.Statistics and Mathematics UnitIndian Statistical InstituteBangaloreIndia

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