On a Huge Family of Non-Schurian Schur Rings

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 fam...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2022-04, Vol.29 (2)
Main Authors: Hanaki, Akihide, Hirai, Takuto, Ponomarenko, Ilia
Format: Article
Language:English
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Summary: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.
ISSN:1077-8926
1077-8926
DOI:10.37236/10696