On schurity of the dihedral group $\boldsymbol{D_{2p}}$
| Autor: | Ryabov, Grigory |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A finite group $G$ is called a Schur group if every $S$-ring over $G$ is schurian, i.e. associated in a natural way with a subgroup of $Sym(G)$ that contains all right translations. One of the crucial open questions in the $S$-ring theory is the question on existence of an infinite family of nonabelian Schur groups. We prove that a dihedral group of order $2p$, where $p$ is a Fermat prime or prime of the form $p=4q+1$, where $q$ is also prime, is Schur. Towards this result, we prove nonexistence of a difference set in a cyclic group of order $p\neq 13$ and classify all $S$-rings over some dihedral groups. Comment: 12 pages |
| Databáze: | arXiv |
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