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This article is cited in 3 scientific papers (total in 3 papers)
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.
Received November 8, 2017, published April 19, 2018
Citation:
I. N. Ponomarenko, G. K. Ryabov, “Abelian Schur groups of odd order”, Sib. Èlektron. Mat. Izv., 15 (2018), 397–411
Linking options:
https://www.mathnet.ru/eng/semr927 https://www.mathnet.ru/eng/semr/v15/p397
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