Explicit Constructions of the non-Abelian p³-Extensions Over \QQ

2008/06/13 by Oz Ben-Shimol, Ben-Shimol, Oz
Computer Science · Mathematics · #11R18 #12F12 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT) #math.NT #msc:11R18 #msc:12F12

paper · pdf · doi:10.48550/arxiv.0806.2202

10 pages. Keywords: Constructive Galois Theory; Heisenberg group, Explicit Embedding problem. Corrections: we revised the proof of Theorem 3.1

openalex publication_date 2008/06/13 · arxiv created 2008/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be an odd prime. Let F/k be a cyclic extension of degree p and of characteristic different from p. The explicit constructions of the non-abelian p³-extensions over k, are induced by certain elements in F(μ_p)^*. In this paper we let k=\QQ and present sufficient conditions for these elements to be suitable for the constructions. Polynomials for the non-abelian groups of order 27 over \QQ are constructed.

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