This article is cited in 3 papers

Mathematical logic, algebra and number theory

Abelian Schur groups of odd order

I. N. Ponomarenko^ab, G. K. Ryabov<sup>cd

a</sup> 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.

UDC: 512.542.3

MSC: 20B30, 05E30

Received November 8, 2017, published April 19, 2018

Language: English

DOI: 10.17377/semi.2018.15.036

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