Geodesic
Characterization of cyclic Schur groups
Algebra i analiz, Tome 25 (2013) no. 5, pp. 61-85.

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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. 
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S. Evdokimov; I. Kovács; I. Ponomarenko. Characterization of cyclic Schur groups. Algebra i analiz, Tome 25 (2013) no. 5, pp. 61-85. http://geodesic.mathdoc.fr/item/AA_2013_25_5_a2/

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