19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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On cyclic Schur groups

Presented by Dr. Istvan KOVACS
Type: Oral presentation
Track: Association Schemes

Content

A finite group $G$ is called a Schur group if all Schur rings over $G$ are schurian, i.e., arise from suitable permutation groups. It is an open problem to characterize the Schur groups, the answer for which is unknown even for cyclic groups. In this talk we prove that if the cyclic group of order $n$ is a Schur group, then $n$ belongs to one of the following five disjoint families of integers: $p^k, pq^k, 2pr^k, pqr, 2pqr,$ where $p,q,r$ are distinct primes, $r$ is odd, and $k$ is an integer greater or equal to $0,1,2$ for the first, second and third family, respectively.

Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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