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 $H &lt;N_G(H)&lt;N_G(N_G(H))\unlhd G$ and $|N_G(N_G(H))|=p<sup>3$ where $p$ is a prime. By a corollary of our main result we obtain some inequality which corresponds to the fact $|G:N_G(N_G(H))|\leq p+1$.