Association schemes with a certain type of p-subschemes

Abstract

In this article, we focus on association schemes with some properties derived from the orbitals of a transitive permutation group G with a one-point stabilizer H satisfying H < N_G(H) < N_G(N_G(H)) ⊴ G and |N_G(N_G(H))| = p³ where p is a prime. By a corollary of our main result we obtain some inequality which corresponds to the fact |G : N_G(N_G(H))| ≤ p + 1.