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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2022, Volume 19, Issue 2, Pages 1077–1087
DOI: https://doi.org/10.33048/semi.2022.19.086 (Mi semr1559) 		 
Mathematical logic, algebra and number theory

On nilpotent Schur groups

G. K. Ryabovab

a Novosibirsk State Technical University, K. Marx avenue, 20, 630073, Novosibirsk, Russia
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/semi.2022.19.086
Abstract: A finite group $G$ is called a Schur group if every $S$-ring over $G$ is schurian, i.e. associated in a natural way with a subgroup of $\mathrm{Sym}(G)$ that contains all right translations. We prove that every nonabelian nilpotent Schur group belongs to one of a few explicitly given families of groups.
Keywords: Schur rings, Schur groups, nilpotent groups.
Funding agency Grant number
Russian Science Foundation 22-71-00021
The work is supported by Russian Scientific Fund (grant 22-71-00021).
Received April 30, 2022, published December 29, 2022
Bibliographic databases:
Document Type: Article
UDC: 512.542.74
MSC: 05E30, 20B25
Language: English
Citation: G. K. Ryabov, “On nilpotent Schur groups”, Sib. Èlektron. Mat. Izv., 19:2 (2022), 1077–1087
Citation in format AMSBIB
\Bibitem{Rya22}
\by G.~K.~Ryabov
\paper On nilpotent Schur groups
\jour Sib. \`Elektron. Mat. Izv.
\yr 2022
\vol 19
\issue 2
\pages 1077--1087
\mathnet{http://mi.mathnet.ru/semr1559}
\crossref{https://doi.org/10.33048/semi.2022.19.086}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4534980}
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