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.
1
Shinshu University
2
St. Petersburg Department of the Steklov Mathematical Institute
Akihide Hanaki; Takuto Hirai; Ilia Ponomarenko. On a huge family of non-Schurian Schur rings. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10696
@article{10_37236_10696,
author = {Akihide Hanaki and Takuto Hirai and Ilia Ponomarenko},
title = {On a huge family of {non-Schurian} {Schur} rings},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {2},
doi = {10.37236/10696},
zbl = {1526.20008},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10696/}
}
TY - JOUR
AU - Akihide Hanaki
AU - Takuto Hirai
AU - Ilia Ponomarenko
TI - On a huge family of non-Schurian Schur rings
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/10696/
DO - 10.37236/10696
ID - 10_37236_10696
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%R 10.37236/10696
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