ERDOS-KO-RADO THEOREM IN SOME LINEAR GROUPS AND SOME PROJECTIVE SPECIAL LINEAR GROUP

Let V be the 2-dimensional column vector space over a finite field F-q, (where q is necessarily a power of a prime number) and let P-q, be the projective line over Fq. In this paper, it is shown that GL(2)(q), for q not equal 3, and SL2(q) acting on V - {0} have the strict EKR property and GL(2)(3) has the EKR property, but it does not have the strict EKR property. Also, we show that GL(n)(q) acting on (F-q)(n) - {0} has the EKR property and the derangement graph of PSL2(q) acting on P-q, where q -1 (mod 4), has a clique of size q + 1.