ERD?S-KO-RADO THEOREM IN SOME LINEAR GROUPS AND SOME PROJECTIVE SPECIAL LINEAR GROUP

摘要

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 F_q. In this paper, it is shown that GL_2(q), for q ≠ 3, and SL_2(q) acting on V — {0} have the strict EKR property and GL2(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 PSL_2(q) acting on P_q, where q ≡ - 1 (mod 4), has a clique of size q + 1.