2021/04/24 by Gareth A. Jones, Jones, Gareth A., Alexander K. Zvonkin +1
Engineering · Mathematics · #05C10 #11G32 #11N13 #11N32 #14H57 #20B20 #20B25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #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.2104.12015
openalex publication_date 2021/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We reinterpret ideas in Klein's paper on transformations of degree 11 from the modern point of view of dessins d'enfants, and extend his results by considering dessins of type (3,2,p) and degree p or p+1, where p is prime. In many cases we determine the passports and monodromy groups of these dessins, and in a few small cases we give drawings which are topologically (or, in certain examples, even geometrically) correct. We use the Bateman-Horn Conjecture and extensive computer searches to support a conjecture that there are infinitely many primes of the form p=(qn-1)/(q-1) for some prime power q, in which case infinitely many groups \rm PSLn(q) arise as permutation groups and monodromy groups of degree p (an open problem in group theory).