On the Finiteness and Structure of Galois Groups of Tamely ramified pro-p Extensions of Imaginary Quadratic Fields

2024/11/05 by Qi Liu, Liu, Qi, Xing, Zugan
Computer Science · Mathematics · #11R11 #11R32 #11R37 #12F10 #20D15 #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2411.03155

openalex publication_date 2024/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a prime p, we study the Galois groups of maximal pro-p extensions of imaginary quadratic fields unramified outside a finite set S, where S consists of one or two finite places not lying above p. When p is odd, we give explicit presentations of these Galois groups under certain conditions. As an application, we determine the structure of the maximal pro-3 extension of ℚ(i) unramified outside two specific finite places.

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