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

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.