Some Erdös-Ko-Rado results for linear and affine groups of degree two
Keywords:derangement graph, independent sets, Erdös-Ko-Rado Theorem, Symmetric Group, General linear group, Affine linear group, Projective linear group
In this paper, we show that both the general linear group GL(2,q) and the special linear group SL(2,q) have both the EKR property and the EKR-module property. This is done using an algebraic method; a weighted adjacency matrix for the derangement graph for the group is found and Hoffman’s ratio bound is applied to this matrix. We also consider the group AGL(2,q) and the 2-intersecting sets in PGL(2,q).