Now showing items 111-120 of 164
Geometric characterization of the sporadic groups Fi22, Fi23, and Fi24
Let Σ1, …, Σ4 be the 3-transposition graphs for Fischer's sporadic groups Fi21, …, Fi24. We classify connected locally Σi graphs gQ = gQi+1 for i = 1, 2, 3. In the minimal case i = 1 we also assume that for every nondegenerate ...
Extending polar spaces of rank at least 3
It is shown that the extended polar space for the sporadic Fischer group Fi22 is the only extended polar space which has more than two extended planes on a block and is not isomorphic to a quotient of an affine polar space ...
New examples of finite C ˜ 2-geometries
The aim of this note is to present a series of examples of finite geometries with diagram, where q=2k and GQ-residues are of type T*2(T ∗ 2 (O) ).
Geometric characterization of graphs from the suzuki chain
Let Σ0,…,Σ6 be the graphs from the Suzuki chain . We classify connected locally Σi graphs Θi + 1 for i = 3, 4, 5. If i = 3, 4 then Θi + 1, is isomorphic to Σi + 1, whereas Θ6 is isomorphic either to Σ6 or to its 3-fold ...
The automorphism group and the convex subgraphs of the quadratic forms graph in characteristic 2
We determine the automorphism group and the convex subgraphs of the quadratic forms graph Quad(n,q),q even.
A sharp exponent bound for McFarland difference sets with p=2
We show that under the self-conjugacy condition a McFarland difference set with p=2 and f≥ in an abelian group G can only exist,if the exponent of the Sylow 2-subgroups does not exceed 4.The method also works for odd p(where ...
Skew-symmetric association schemes with two classes and strongly regular graphs of type L 2n-1(4n-1)
A construction of a pair of strongly regular graphs Γn and Γ'n of type L 2n-1 (4n-1) from a pair of skew-symmetric association schemes W, W' of order 4n-1 is presented. Examples of graphs with the same parameters as Γn and ...
Subsets close to invariant subsets for group actions
Let G be a group acting on a set Ω and k a non-negative integer. A subset (finite or infinite) A ⊆ Ω is called k-quasi-invariant if |Ag \ A| ≤k for every g ∈ G. It is shown that if A is k-quasi-invariant for k ≥1 , then ...
Cyclotomic integers and finite geometry
We obtain an upper bound for the absolute value of cyclotomic integers which has strong implications on several combinatorial structures including (relative) difference sets, quasiregular projective planes, planar functions, ...
Multiple extensions of generalized hexagons related to the simple groups McL and Co3
The groups McL, Co3 and 2 × Co3 are all contained in the automorphism group of a 2-, respectively, 3-fold extension of a generalized hexagon of order (4,1). We give a geometric characterization of these multiple extensions ...