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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 397–411 (Mi semr927)  

Mathematical logic, algebra and number theory

Abelian Schur groups of odd order

I. N. Ponomarenkoab, G. K. Ryabovcd

a St.Petersburg State University, Universitetskaya Emb., 13B, 199034, St. Petersburg, Russia
b St. Petersburg Department of the Steklov Mathematical Institute, Fontanka, 27, 191023, St. Petersburg, Russia
c Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
d Novosibirsk State University, Pirogova, 1, 630090, Novosibirsk, Russia

Abstract: A finite group $G$ is called a Schur group if any Schur ring over $G$ is associated in a natural way with a subgroup of $\mathrm{sym} (G)$ that contains all right translations. It is proved that the group $C_3\times C_3\times C_p$ is Schur for any prime $p$. Together with earlier results, this completes a classification of the abelian Schur groups of odd order.

Keywords: Schur rings, Schur groups, permutation groups.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-51-53007_GFEN_a
Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01
Russian Science Foundation 14-21-00065
The work of the first author was supported by the RFBR Grant No. 17-51-53007 GFEN a and by the Program of the Presidium of the Russian Academy of Sciences No. 01 Fundamental Mathematics and its Applications under grant PRAS-18-01. The second author was supported by RSF (project No. 14-21-00065).


DOI: https://doi.org/10.17377/semi.2018.15.036

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Bibliographic databases:

Document Type: Article
UDC: 512.542.3
MSC: 20B30, 05E30
Received November 8, 2017, published April 19, 2018
Language: English

Citation: I. N. Ponomarenko, G. K. Ryabov, “Abelian Schur groups of odd order”, Sib. Èlektron. Mat. Izv., 15 (2018), 397–411

Citation in format AMSBIB
\Bibitem{PonRya18}
\by I.~N.~Ponomarenko, G.~K.~Ryabov
\paper Abelian Schur groups of odd order
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 397--411
\mathnet{http://mi.mathnet.ru/semr927}
\crossref{https://doi.org/10.17377/semi.2018.15.036}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438412200036}


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