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

Authors:
Binod Kumar Sahoo;N. S. Sastry
Affiliations:
Department of Mathematics, National Institute of Technology, Rourkela, India 769008;Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore, India 560059
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2009

Citing 4
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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|=2 β , 1+NPdim(S)驴β驴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.