Minimal Ramification in Nilpotent Extensions

2010/07/22 by Nadya Markin, Markin, Nadya, Stephen V. Ullom +1
Computer Science · Mathematics · #11R32 #11S31 #12F10 #12F12 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1007.3933

openalex publication_date 2010/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite nilpotent group and K a number field with torsion relatively prime to the order of G. By a sequence of central group extensions with cyclic kernel we obtain an upper bound for the minimum number of prime ideals of K ramified in a Galois extension of K with Galois group isomorphic to G. This sharpens and extends results of Geyer and Jarden and of Plans. Also we confirm Boston's conjecture on the minimum number of ramified primes for a family of central extensions by the Schur multiplicator.

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