On some locally 3-transposition graphs
Pasechnik, Dmitrii V.
Date of Issue1993
Finite Geometry and Combinatorics (2nd : 1993 : Deinze, Belgian)
School of Physical and Mathematical Sciences
Let ∑_n^ε be the graph defined on the (+)- points of an n-dimensional GF(3)-space carrying a nondegenerate symmetric bilinear form with discriminant ε, points are adjacent if they are perpendicular. We prove that if ε = 1, n ≥ 6 (resp.ε=-1,n≥7) then ∑_(n+1)^εis the unique connected locally ∑_n^ε graph. One may view this result as a characterization of a class of c^k. C_2-geometries (or 3-transposition groups). We briefly discuss an application of the result to a characterization of Fischer's sporadic groups.
© 1993 Cambridge University Press. This paper was published in Finite geometry and combinatorics and is made available as an electronic reprint (preprint) with permission of Cambridge University Press. The paper can be found at the following DOI: http://dx.doi.org/10.1017/CBO9780511526336.030. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.