Vol. 9, No. 1, 2009

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A non-abelian representation of the dual polar space $DQ(2n,2)$

Kamal Lochan Patra and Binod Kumar Sahoo

Vol. 9 (2009), No. 1, 177–188
DOI: 10.2140/iig.2009.9.177
Abstract

We prove that the dual polar space DQ(2n,2), n 3, of rank n associated with a non-singular parabolic quadric in PG(2n,2) admits a faithful non-abelian representation in the extraspecial 2-group 2+1+2n . The near 2n-gon In (section 2.4) is a geometric hyperplane of DQ(2n,2). For n 3, we first construct a faithful non-abelian representation of In in 2+1+2n and subsequently extend it to a faithful non-abelian representation of DQ(2n,2) in 2+1+2n .

Keywords
dual polar space, non-abelian representation, extraspecial 2-group
Mathematical Subject Classification 2000
Primary: 05B25
Milestones
Received: 20 July 2007
Accepted: 27 March 2008
Authors
Kamal Lochan Patra
Binod Kumar Sahoo