Geodesic
On the order of a non-Abelian representation group of a slim dense near hexagon
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 2, pp. 195-213.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $| R|=2 ^{ \beta }, 1+ NPdim( S)\leq \beta \leq 1+ dimV( S)$, 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 $\beta =1+ NPdim( S)$, 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: keywords near polygons, non-abelian representations, generalized quadrangles, extraspecial 2-groups 
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     author = {Sahoo, Binod Kumar and Sastry, N.S.Narasimha},
     title = {On the order of a {non-Abelian} representation group of a slim dense near hexagon},
     journal = {Journal of Algebraic Combinatorics},
     pages = {195--213},
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Sahoo, Binod Kumar; Sastry, N.S.Narasimha. On the order of a non-Abelian representation group of a slim dense near hexagon. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 2, pp. 195-213. http://geodesic.mathdoc.fr/item/JAC_2009__29_2_a3/