2021/06/01 by Gareth Jones, Jones, Gareth A., Alexander K. Zvonkin +1
Computer Science · Engineering · Mathematics · #11A41 #11N05 #11N32 #20B05 #20B25 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Number Theory (math.NT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2106.00346
openalex publication_date 2021/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (qn-1)/(q-1) of \rm PSLn(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≥ 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 PSLn(q), \rm PSUn(q) and \rm PSp2n(q) which arise in the work of Dixon and Zalesskii on linear groups of prime degree.