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Association schemes with a certain type of $p$-subschemes

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arxiv 2112.02911 v1 pith:XUK2RRCJ submitted 2021-12-06 math.CO

classification math.CO
keywords associationschemessomearticlecertaincorollarycorrespondsderived
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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 $H <N_G(H)<N_G(N_G(H))\unlhd G$ 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 $|G:N_G(N_G(H))|\leq p+1$.

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