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

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

2006-12-18

arxiv.org/abs/math/0612513v1

Journal of Algebraic Combinatorics, 29 (2009), 195-213

Mathematics

Combinatorics

Scientific paper

10.1007/s10801-008-0129-0

We show that, if the representation group $R$ of a slim dense near hexagon $S$ is non-abelian, then $R$ is 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 an extraspecial 2-group (Theorem 1.6).

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