On some locally 3-transposition graphs - Pasechnik, Dmitrii V. (2011)
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.