Association schemes with a certain type of p-subschemes

Wasim Abbas, Mitsugu Hirasaka

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 < NG(H) < NG(NG(H)) ⊴ G and |NG(NG(H))| = p3 where p is a prime. Our main result is if (Ω, S) is an association scheme with Oθ(S) < Oθ(S) such that ns ∈ {1, p} for each s ∈ S and nOθ(S) = p2 where p is a prime, then |Ω| ≤ p2(p + 1). By a corollary of our main result we obtain some inequality which corresponds to the fact |G : NG(NG(H))| ≤ p + 1.


Keywords


Coherent configurations, association schemes, p-schemes.

Full Text:

MANUSCRIPT


DOI: https://doi.org/10.26493/1855-3974.2034.dad

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications