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 ))| =  p 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 ))| ≤  p  + 1 .