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arXiv · 2109.01385

On a huge family of non-schurian Schur rings

Akihide Hanaki·Takuto Hirai·Ilia Ponomarenko
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Abstract

In his famous monograph on permutation groups, H.~Wielandt gives an example of a Schur ring over an elementary abelian group of order $p^2$ ($p>3$ is a prime), which is non-schurian, that is, it is the transitivity module of no permutation group. Generalizing this example, we construct a huge family of non-schurian Schur rings over elementary abelian groups of even rank.

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Akihide Hanaki, Takuto Hirai, Ilia Ponomarenko. 2021-09-03. On a huge family of non-schurian Schur rings. https://doi.org/10.37236/10696

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