Groups of prime degree and the Bateman-Horn Conjecture
| Autor: | Jones, Gareth A., Zvonkin, Alexander K. |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | As a consequence of the classification of finite simple groups, the classification of permutation groups of prime degree is complete, apart from the question of when the natural degree $(q^n-1)/(q-1)$ of ${\rm PSL}_n(q)$ is prime. We present heuristic arguments and computational evidence based on the Bateman-Horn Conjecture to support a conjecture that for each prime $n\ge 3$ there are infinitely many primes of this form, even if one restricts to prime values of $q$. Similar arguments and results apply to the parameters of the simple groups ${\rm PSL}_n(q)$, ${\rm PSU}_n(q)$ and ${\rm PSp}_{2n}(q)$ which arise in the work of Dixon and Zalesskii on linear groups of prime degree. Comment: 18 pages. New applications to linear groups, error-correcting codes and difference sets added. Modified title |
| Databáze: | arXiv |
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