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This article is cited in 13 scientific papers (total in 13 papers)
Research Papers
Characterization of cyclic Schur groups
S. Evdokimova, I. Kovácsb, I. Ponomarenkoa a St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka, 27, 191023, St. Petersburg, Russia
b IAM and FAMNIT, University of Primorska, Muzejski trg 2, SI6000, Koper, Slovenia
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 was proved by R. Pöschel (1974) that, given a prime $p\ge5$, a $p$-group is Schur if and only if it is cyclic. We prove that a cyclic group of order $n$ is Schur if and only if $n$ belongs to one of the following five families of integers: $p^k$, $pq^k$, $2pq^k$, $pqr$, $2pqr$ where $p,q,r$ are distinct primes, and $k\ge0$ is an integer.
Keywords:
Schur ring, Schur group, permutation group, circulant cyclotomic S-ring, generalized wreath product.
Received: 07.09.2012
Citation:
S. Evdokimov, I. Kovács, I. Ponomarenko, “Characterization of cyclic Schur groups”, Algebra i Analiz, 25:5 (2013), 61–85; St. Petersburg Math. J., 25:5 (2014), 755–773
Linking options:
https://www.mathnet.ru/eng/aa1354 https://www.mathnet.ru/eng/aa/v25/i5/p61
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Abstract page: | 262 | Full-text PDF : | 58 | References: | 39 | First page: | 13 |
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