Coset closure of a circulant S-ring and schurity problem
| Autor: | Evdokimov, Sergei, Ponomarenko, Ilya |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Journal of Algebra and Its Applications, {\bf 15}, No. 4 (2016), Article ID 1650068, 49 pp |
| Druh dokumentu: | Working Paper |
| Popis: | Let $G$ be a finite group. There is a natural Galois correspondence between the permutation groups containing $G$ as a regular subgroup, and the Schur rings (S-rings) over~$G$. The problem we deal with in the paper, is to characterize those S-rings that are closed under this correspondence, when the group $G$ is cyclic (the schurity problem for circulant S-rings). It is proved that up to a natural reduction, the characteristic property of such an S-ring is to be a certain algebraic fusion of its coset closure introduced and studied in the paper. Basing on this characterization we show that the schurity problem is equivalent to the consistency of a modular linear system associated with a circulant S-ring under consideration. As a byproduct we show that a circulant S-ring is Galois closed if and only if so is its dual. Comment: 42 pages |
| Databáze: | arXiv |
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