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Normal cyclotomic schemes over a finite commutative ring

Sergei Evdokimov·Ilia Ponomarenko
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Abstract

We study cyclotomic association schemes over a finite commutative ring $R$ with identity. The main interest for us is to identify the normal cyclotomic schemes $C$, i.e. those for which $Aut(C)$ is a subgroup of the one-dimensional affine semilinear group over $R$. The problem is reduced to the case when the ring $R$ is local in which a necessary condition of normality in terms of the subgroup of $R^\times$ defining $C$, is given. This condition is proved to be sufficient for a class of local rings including the Galois rings of odd characteristic.

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Sergei Evdokimov, Ilia Ponomarenko. 2006-08-18. Normal cyclotomic schemes over a finite commutative ring. https://arxiv.org/abs/math/0608469

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