Graphs, Geometry, 3-transpositions, and Symplectic F2-transvection Groups
نویسنده
چکیده
In this paper we begin the classification completed in [12] of all partial linear spaces n , graphs F, and groups G which satisfy one of the following: I. II = (0>, ££) is a connected partial linear space of order 2 in which every pair of intersecting lines lies in a subspace isomorphic to the dual of an affine plane of order 2; II. F is a connected graph such that, for each vertex x of F, the set of vertices of T adjacent to x forms a subgraph isomorphic to a grid graph L(3, Ax), where A* is a set depending on x;
منابع مشابه
On the geometry of k-transvection groups
More than 20 years ago, B. Fischer [5,6] started his pioneering work on groups generated by a conjugacy class of 3-transpositions, i.e., a conjugacy class of involutions D, such that for all d, e ∈ D, we have that [d, e] = 1 or 〈d, e〉 ' SL2(2). Fischer classified all finite groups G generated by a class of 3-transpositions under the additional assumptions that G′′ = G′ and O2(G) = O3(G) = Z(G) ...
متن کاملSwitched symplectic graphs and their 2-ranks
We apply Godsil–McKay switching to the symplectic graphs over F2 with at least 63 vertices and prove that the 2-rank of (the adjacency matrix of) the graph increases after switching. This shows that the switched graph is a new strongly regular graphwith parameters (22ν−1, 22ν−1, 22ν−2, 22ν−2) and 2-rank 2ν+2 when ν ≥ 3. For the symplectic graph on 63 vertices we investigate repeated switching b...
متن کاملFlat graphs based on affine spaces and affine symplectic spaces
Let AG(n,Fq) be the n-dimensional affine space over the finite field Fq. For 0 ≤ m ≤ n − 1, define a graph G whose vertex set is the set of all m-flats of AG(n,Fq), such that two vertices F1 and F2 are adjacent if dim(F1∨F2) = m+1, where F1∨F2 is the minimum flat containing both F1 and F2. Let ASG(2ν,Fq) be the 2ν-dimensional affine-symplectic space over Fq. Define a graph S (ν) whose vertex se...
متن کاملInternational Conference on Incidence Geometry
1. Kristina Altmann, Hyperbolic lines in unitary space. 2. John Bamberg, Transitive m-systems. 3. Barbara Baumeister, The primitive permutation groups with a regular subgroup. 4. Rieuwert Blok, Extensions of isomorphisms for affine grassmannians over F2. 5. Matthew Brown, Tetradic sets of elliptic quadrics of PG(3, q) and generalized quadrangles of order (s, s2) with Property (G). 6. Julia Brow...
متن کامل2 S ep 2 00 3 Compactness results in Symplectic Field Theory
This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in [EGH]. We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic Field Theory. The theorems generalize Gromov's compactness theorem in [Gr] as well as compactness theorems in Floer homology theory, [F1, F2], and in contact geometry, [H, HWZ8].
متن کامل