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arXiv · 2010.08023

Primes in geometric series and finite permutation groups

Gareth A. Jones·Alexander K. Zvonkin
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Abstract

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 ${\rm L}_n(q)$ is prime. We present heuristic arguments and computational evidence 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 $q$.

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Gareth A. Jones, Alexander K. Zvonkin. 2020-10-15. Primes in geometric series and finite permutation groups. https://arxiv.org/abs/2010.08023

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