Let G be a group acting faithfully and transitively on Ω i for i = 1, 2. A famous theorem by Burnside implies the following fact: If ∣Ω 1∣ = ∣Ω 2∣ is a prime and the rank of one of the actions is greater than two, then the actions are equivalent, or equivalently ∣(α, β)G∣ = ∣Ω 1∣ = ∣Ω 2∣ for some (α, β) ∈ Ω 1 × Ω 2.In this paper we consider a combinatorial analogue to this fact through the theory of coherent configurations, and give some arithmetic sufficient conditions for a coherent configuration with two homogeneous components of prime order to be uniquely determined by one of the homogeneous components.
@article{769,
title = {Coherent configurations over copies of association schemes of prime order},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {12},
year = {2016},
doi = {10.26493/1855-3974.769.47d},
language = {EN},
url = {http://dml.mathdoc.fr/item/769}
}
Sharafdini, Reza; Hirasaka, Mitsugu. Coherent configurations over copies of association schemes of prime order. ARS MATHEMATICA CONTEMPORANEA, Tome 12 (2016) . doi : 10.26493/1855-3974.769.47d. http://gdmltest.u-ga.fr/item/769/